- Email: [email protected]
Research on personal financial data storage medium system based on fractional order calculus encryption algorithm
ARTICLE IN PRESS
JID: CHAOS
[m5G;October 18, 2019;15:17]
Chaos, Solitons and Fractals xxx (xxxx) xxx
Contents lists available at ScienceDirect
Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena journal homepage: www.elsevier.com/locate/chaos
Research on personal financial data storage medium system based on fractional order calculus encryption algorithm Yue Yin∗, Luyao Wang Academy of Economic Shanghai University, Shang Hai, 200041, China
a r t i c l e
i n f o
Article history: Received 24 July 2019 Revised 20 September 2019 Accepted 25 September 2019 Available online xxx AMS 2010 codes: 34C15 37D45
a b s t r a c t The paper studies the chaotic synchronization problem of fractional calculus financial system. At the same time, according to the requirements of bank ATM for port security and the security management of mobile storage media, the fractional calculus encryption algorithm is applied to the personal financial data storage medium system. Authorize and manage mobile storage devices to protect against the use risks and security threats caused by mobile storage devices. The research of the thesis shows that the system has certain applicability and can guarantee the security of personal financial data. Simulation examples show the effectiveness of the method. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Fractional calculus Personal financial data storage Media system research Financial data system
1. Introduction China’s self-service equipment has a large number of holdings, and its growth momentum is strong, which plays a prominent role in people’s daily lives. At the end of 2011, the global ATM holding capacity will reach 2 million units, of which China’s ATM reserves will reach 330,0 0 0 units, and the daily processing of cash will exceed 45 billion yuan [1]. Since China’s per capita possession is seriously lower than that of developed countries, and the urban-rural distribution is extremely uneven, there will be a lot of room for ATM growth in China in the next few years, especially in the vast rural areas. At the same time, China’s bank card demand is large. At the end of 2010, the number of bank cards issued in China has reached 2.4 billion, with 1.4 per capita. ATM demand will further increase. In the past five years, the number of selfservice devices has grown at a rate of more than 22% per year. It is estimated that China will have 540,0 0 0 units in 2015. A large number of self-service equipment as an important part of a country’s financial infrastructure has laid an important role in social security and stability. With the development of information technology, U disk and other peripheral mobile storage media have been widely used in ATM maintenance, but in the process of using mobile storage media, such as unauthorized use, internal use, and viruses the
∗
Corresponding author. E-mail address: [email protected] (Y. Yin).
risk of loss or theft of mobile storage media can pose a considerable security risk to ATMs [2]. The theory of fractional calculus operator has been successfully applied in physics, solving many problems in the field of physics. In the past ten years, the fractional calculus theory that has been successfully applied in physics has also been successfully applied in the fields of humanities and social sciences, such as fractional financial models, fractional happiness models, and fractional love models. In view of the above risk problems, we propose a personal financial data mobile storage medium management scheme based on fractional calculus encryption algorithm to realize risk prevention and security management of various mobile storage media [3].
2. Application of fractional calculus in financial system When attending the 2010 Asian Financial Forum, President of the International Monetary Fund, Kahn pointed out that compared with developed countries, the local demand of emerging market economies is more flexible, the economic structure is better, and the unit investment cost is relatively low. Thus, for system (1), we can conservatively assume that c − b − abc0 is one of the characteristics of some emerging market economies. Compared with emerging market economies, the economic structure of developed countries is relatively mature, the elasticity of domestic commodity demand is not high enough, and the unit investment cost is relatively high [4]. Thus, for system (1), we can conservatively
https://doi.org/10.1016/j.chaos.2019.109459 0960-0779/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Y. Yin and L. Wang, Research on personal financial data storage medium system based on fractional order calculus encryption algorithm, Chaos, Solitons and Fractals, https://doi.org/10.1016/j.chaos.2019.109459
ARTICLE IN PRESS
JID: CHAOS 2
[m5G;October 18, 2019;15:17]
Y. Yin and L. Wang / Chaos, Solitons and Fractals xxx (xxxx) xxx
believe that some non-emerging market economies will have the characteristics of c − b − abc ≤ 0. In order to study the fractional form of the system (1), the following Laplace differential form is used: As fractional differential equations appear more and more frequently in engineering applications, effective and simple solution methods for fractional differential equations are becoming more and more important. However, existing methods have various methods. defect. In the following, we introduce a method for solving fractional differential equations based on Laplace transform. This method is simple and intuitive, and is suitable for solving linear fractional differential equations with constant coefficients. 2.1. Laplace transform method Application of Laplace transform method Below we use two examples to illustrate the application of the Laplace transform method. The paper considers the Laplace
transform method to solve the initial value problem of the nonhomogeneous standard fractional differential equations as follows. α y (t ) − λy (t ) = h (t ), (t > 0 )
0 Dt
(1)
[0 Dtα −k y(t )]t=0 = bk , (k = 1, 2, · · · , n ) n−1<α
(2)
Solution: Perform a Laplace transform on both ends of Eq. (1) and use the initial value condition (2) to get:
sα Y (s ) − λY (s ) = H (s ) +
n
bk sk−1
H (s ) Y (s ) = α + s −λ
k=1
(4)
y(t ) =
The Laplace inverse transformation of Eq. (9) gives the solution of the original differential equation as:
y(t ) = b2 t α1 −1 Eα ,α1 (λt α ) + b1 t α −1 Eα ,α (λt α ) t
t 0
(t − τ )α−1 Eα,α (λ(t − τ )α )h(τ )dτ
Among them, α = α1 + α2 . Note: Comparing the above two initial value problems, it is easy to see that they are very similar in form. The only difference is reflected in a standard fractional differential equation based on classical fractional calculus, one based on the sequence fractional calculus. Sequence fractional differential equations, which are different in the initial value. But we found that their solutions are also very similar in expression, the comparison results are as follows:
In the theoretical analysis part of fractional differential equations, we mainly introduce two aspects, one is the nature of the solution of fractional differential equations, and the other is the solution method of fractional differential equations [6]. Since the research on fractional differential equations is not mature enough, the theoretical analysis made is still in the exploratory stage. Most of the existing results are simple extensions of classical calculus equation theory, and can only cover some special forms of fractional differential equations. Much of the existing work is trying to find new theoretical methods to break the existing constraints and strive to construct a complete set of fractional differential equation theory.
Any order integral definition: Let P<0, if f(x) is m+1 order continuous, −p a Dt
f (x ) =
= (5)
Note: The process of solving this problem by iterative method is also given in some literatures. Although the results of the two solutions are the same, it is obvious that the Laplace solution method is more intuitive and simpler. Below we consider the Laplace transform method to solve the initial value problem of the sequence fractional differential equations [5]. α2
(0 Dtα1 y(t )) − λy(t ) = h(t )
[0 Dtα2 −1 (0 Dtα1 y(t ))]t=0 = b1 , [0 Dtα1 −1 y(t )]t=0 = b2
(7)
(8)
p
lim h h→0 nh = t − a
n p r f (t − rh ) r=0
m p+k f (k ) (a )(t − a ) ( p + k + 1 ) k=0 t 1 + (t − τ )−p+m f (m+1) (τ )dτ ( p + k + 1 ) a
(11)
Any order differential definition: Let p>0, if on [a, t], f(k) (t), (k=1,2,...,m+1) is continuous, and m>p-1, for m, the minimum value of p depends on m
f (x ) =
(6)
Perform a Laplace transform on both ends of Eq. (6) and use the initial value condition (7) to get:
(sα1 +α2 − λ )Y (s ) = H (s ) + sα2 b2 − b1
(10)
0
bk t α −k Eα ,α −k+1 (λt α )
0 Dt
(t − τ )α−1 Eα,α (λ(t − τ )α )h(τ )dτ
+
k=1
+
(9)
The Laplace inverse transformation of the formula (3) can obtain the solution of the original differential equation as: n
H (s ) + sα2 b2 + b1 sα2 +α1 − λ
2.2. Grunwald-Letnikow fractional calculus:
k−1
s bk α s −λ
Y (s ) =
(3)
k=1 n
There is:
=
lim fhp (t ) h→0 nh = t − a m −p+k f (k ) (a )(t − a ) (−p + k + 1 ) k=0 t 1 + (t − τ )−p+m f (m+1) (τ )dτ (−p + k + 1 ) a
(12)
Please cite this article as: Y. Yin and L. Wang, Research on personal financial data storage medium system based on fractional order calculus encryption algorithm, Chaos, Solitons and Fractals, https://doi.org/10.1016/j.chaos.2019.109459
JID: CHAOS
ARTICLE IN PRESS
[m5G;October 18, 2019;15:17]
Y. Yin and L. Wang / Chaos, Solitons and Fractals xxx (xxxx) xxx
3. Research and development of fractional calculus personal financial data storage system 3.1. Deployment network diagram Take a provincial branch application as an example. The deployed network architecture is shown in Fig. 1: Following the SOA design concept, the state-owned bank data centralized management system is divided into four system domains: business support, operational support, outreach and management information. The business support system domain includes an acceptance system, a transaction processing system, and an accounting processing system; the operation support system domain includes a common code management system, an operation management system, a monitoring system, and a hot backup and automatic recovery system; the external system domain includes a communication system and an agent. Business interface system, UnionPay system [7]; Management information system domain includes report processing system, historical query system, intelligent decision system and service information system. Each system works together through the application integration platform to support the operation and management of state-owned banks. The overall architecture has the characteristics of “loose coupling, high cohesion”, flexible deployment, stable and reliable, and strong scalability [8]. The system handles intermediate processes such as calculating interest in banking and generating various registration books. The generated accounting information is submitted to the accounting processing system for billing. The accounting is separated from the transaction processing system, which shortens the transaction processing time, avoids resource problems such as excessive transaction processing time due to complex intermediate processes such as interest-bearing in the centralized management system transaction, and improves the processing efficiency of the transaction. The data exchange system functions as an Enterprise Service Bus
3
(ESB). The system uses the loose coupling of message packets to implement information exchange between different services. The management service system provides management services such as system monitoring and fund monitoring. 3.2. Mobile storage media protection (1) System administrator. Municipal branch IT administrator. Filter the USB device usage requirements of ATM maintainers. Create authorizations, distribute authorizations, delete authorizations, and change authorizations for USB licenses. Manage registered devices for USB licenses created: USB loss/deactivation, USB enabled, USB usage statistics. (2) Super administrator. Provincial branch IT administrator. For the management of the System Administrator, configure the number of USB authorization codes and authorization roles that the System Administrator can generate. Management of USB authorization roles: create new roles, delete roles, and modify roles. Manage authorized USB usage: USB loss/deactivation, USB enabled, USB usage statistics. (3) ATM maintenance personnel. USB device user. Authorization registration and use of USB devices. The hierarchical relationship between the roles is shown in Fig. 2. 3.3. Mobile storage media management system Business Management System: Handling services that need to be handled by operators, including manual entry, review, supervision, authorization, group submission, query printing, data import and export, etc., and retain the necessary information. Transaction Processing System: Processing various services submitted by the data exchange system, including control of transaction scheduling, quota, etc., generation of income and expenditure register, processing of transaction information, generation of accounting vouchers, etc. Accounting processing system: Processing
Fig. 1. System network architecture.
Please cite this article as: Y. Yin and L. Wang, Research on personal financial data storage medium system based on fractional order calculus encryption algorithm, Chaos, Solitons and Fractals, https://doi.org/10.1016/j.chaos.2019.109459
ARTICLE IN PRESS
JID: CHAOS 4
[m5G;October 18, 2019;15:17]
Y. Yin and L. Wang / Chaos, Solitons and Fractals xxx (xxxx) xxx
Fig. 2. System administrator and user rights.
billing, inventory, generating receipts, etc. submitted by the data exchange system, batch processing at the beginning and end of the day, responsible for the generation of the running account, the household account, and the general ledger. External communication system: mainly responsible for compiling, generating messages, pledging, decomposing messages, converting message formats, exchanging with other system messages, etc.; running management system: responsible for public parameter code management, operation monitoring, log management, Data management and operator login and sign-off management. Report Processing System: Responsible for collecting and processing data, generating and displaying reports. Historical Query System: Collect and save historical information of the system, such as original vouchers, accounting vouchers, register information, etc. [9]. Data exchange system: Responsible for the communication between the various systems within the data central management system, including receiving the packets sent by each system, performing the necessary processing on the packets, and forwarding the packets to the destination system.
be obtained by substituting partial differential equations:
3.4. Mobile storage media usage process (1) Generate authorization code: According to the needs of ATM maintenance personnel, the bank management personnel can generate the authorization code with the corresponding role authority and aging time through the management background and deliver it to the corresponding personnel. (2) Registration authorization code: ATM maintenance personnel insert the unknown mobile storage device into ATM for the first time, need to register, input legal authorization code and corresponding registration information to complete registration.
4. Financial media system simulation 4.1. Numerical solution - implicit format At present, it is important to study the problem of heat conduction, especially the problem of unsteady heat conduction. The implicit format is used here. Using u(x, t), the forward difference quotient for t: (U kj +1 − U kj )/ t; the second-order center difference for x: +1 +1 (U kj+1 − 2U kj +1 + U kj−1 )/(x )2 .
Implicit
Fig. 3. Numerical solution of the velocity equation of the financial system.
difference
format
can
U jk+1 − U jk t
=
k+1 k+1 U j+1 − 2U jk+1 + U j−1
(x )2
(13)
4.2. Numerical solution - analysis and MATLAB implementation (1) The financial system response time is 2 seconds. The design space step size is h=0.1 and the time step is t=0.01, and the grid ratio is r = t/h2 . Thus, the number of spatial grid points obtained is M1+1, and the number of time grid points is M2 + 1. First set the initial time matrix U (M2 + 1, M1 + 1). The boundary conditions and initial conditions are then written into a matrix representing the running speed distribution. The specific code can be seen in the final appendix (2) Write matrix A. Core code: Diagonal: A (i, j) = 1 + 2r diagonally to the right and below: A (i, i+1) = -r; A (i+1, j) = -r; The following is the use of B to iterate [10]. When k=1, A∗ U (2, j) =U (1, j) When k=2, A∗ U (3, j) =U (2, j) When k=3, A∗ U (4, j) =U (3, j)
Please cite this article as: Y. Yin and L. Wang, Research on personal financial data storage medium system based on fractional order calculus encryption algorithm, Chaos, Solitons and Fractals, https://doi.org/10.1016/j.chaos.2019.109459
JID: CHAOS
ARTICLE IN PRESS
[m5G;October 18, 2019;15:17]
Y. Yin and L. Wang / Chaos, Solitons and Fractals xxx (xxxx) xxx
Fig. 4. Financial data system processing speed graph for numerical solution of smooth transition.
5
Fig. 7. Numerical solution and analytical solution space error (3D map).
Fig. 5. MATLAB running screenshot.
Fig. 8. Numerical solution and analytical solution time error (two-dimensional map).
Fig. 6. Solution processing speed map.
This iteration continues until k=M2 . The distribution matrix U of the processing speed of the banking system over time and space can be obtained. (3) Numerical solution, as shown in Figs. 3 and 4. Now the coloring transitions smoothly. 4.3. Comparison of numerical solutions and analytical solutions Firstly, we need to discretize the analytical solution. There is 2 2 an e−n π t in the analytical solution. When n is getting bigger, it will quickly go to 0, so we can take n=80 0 0. Now to prove the feasibility, the workspace calculation in MATLAB. Draw the running speed distribution of the analytical solution, and numerically draw the drawing, as shown in Fig. 6.
The numerical solution is subtracted from the analytical solution to obtain an error map. As shown in Figs. 7 and 8, we can see the spatial error from Fig. 7, and the error is large at the boundary [11]. We can see the error of time from Fig. 8. At the beginning of the time, the error is the largest, then there is a small fluctuation, and finally the error gradually becomes smaller, and finally it goes to zero [12]. 5. Conclusion Economic chaos is an inherent uncertainty in economic and financial systems. It is an extremely complex phenomenon that often appears in this system and is an important part of current nonlinear economic dynamics research. This paper qualitatively studies the personal financial data storage medium system based on fractional calculus encryption algorithm, and numerically simulates the influence of the savings amount and differential order on the evolution behavior of the fractional financial system complexity, and draws some meaningful results. The research results can provide a theoretical basis for the government to regulate the economic and financial system. In addition, this software implements the software program by using C language programming. The
Please cite this article as: Y. Yin and L. Wang, Research on personal financial data storage medium system based on fractional order calculus encryption algorithm, Chaos, Solitons and Fractals, https://doi.org/10.1016/j.chaos.2019.109459
JID: CHAOS 6
ARTICLE IN PRESS
[m5G;October 18, 2019;15:17]
Y. Yin and L. Wang / Chaos, Solitons and Fractals xxx (xxxx) xxx
software has a wide range of practical engineering prospects through the authorization and management of USB storage devices to prevent the use risks and security threats caused by USB storage devices. Declaration of Competing Interest None. References [1] Smirnov V, Volchenkov D. Five years of phase space dynamics of the standard & poor’s 500. Appl Math Nonlinear Sci 2019;4(1):203–16. [2] González JLR, López JAV, Martínez MF. Raptors “right hunger” characterization to develop sustainable exclusion areas for wildlife at civil & military airports. Appl Math Nonlinear Sci 2018;1(2):335–44. [3] Baskonus HM, Bulut H, Sulaiman TA. New complex hyperbolic structures to the lonngren-wave equation by using sine-gordon expansion method. Appl Math Nonlinear Sci 2019;4(1):141–50. [4] BAGLEY RL. Power law and fractional calculus model of viscoelasticity. AIAA J 1989;27(10):1412–17.
[5] Gutiérrez-Carvajal, de Melo RE, Flávio L, Rosário, Maurício J, Machado, Tenreiro JA. Condition-based diagnosis of mechatronic systems using a fractional calculus approach. Int J Syst Sci 2016;47(9):2169–77. [6] Rahmani Fazli H, Hassani F, Ebadian A, Khajehnasiri AA. National economies in state-space of fractional-order financial system. Afrika Matematika 2016;27(3–4):529–40. [7] Bingsan, Chen, Chunyu, Benjamin, Wilson, Yijian, et al. Fractional modeling and analysis of coupled mr damping system. IEEE/CAA J Automat Sinica 2016;3(3):288–94. [8] TAKAMATSU T, OHMORI H. Online parameter estimation for lithium-ion battery by using adaptive observer for fractional-order system. Electron Commun Japan 2017;137(8):1015–23. [9] Tirandaz H, Karami-Mollaee A. On active synchronization of fractional-order bloch chaotic system and its practical application in secure image transmission. Int J Intell ComputCybern 2018;11(2):181–96. [10] Liang, Gui-shu J, Yong-ming L, Zong-en, Liu X, Ma L. Modelling of frequency characteristics of the oil-paper compound insulation based on the fractional calculus. Iet Sci Measur Technol 2017;11(5):646–54. [11] Huang C, Duan JS. Steady-state response to periodic excitation in fractional vibration system. J Mech 2016;32(1):25–33. [12] Kaslik, Eva. Analysis of two- and three-dimensional fractional-order hindmarsh-rose type neuronal models. Fract Calculus Appl Anal 2017;20(3):623–45.
Please cite this article as: Y. Yin and L. Wang, Research on personal financial data storage medium system based on fractional order calculus encryption algorithm, Chaos, Solitons and Fractals, https://doi.org/10.1016/j.chaos.2019.109459
JID: CHAOS
[m5G;October 18, 2019;15:17]
Chaos, Solitons and Fractals xxx (xxxx) xxx
Contents lists available at ScienceDirect
Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena journal homepage: www.elsevier.com/locate/chaos
Research on personal financial data storage medium system based on fractional order calculus encryption algorithm Yue Yin∗, Luyao Wang Academy of Economic Shanghai University, Shang Hai, 200041, China
a r t i c l e
i n f o
Article history: Received 24 July 2019 Revised 20 September 2019 Accepted 25 September 2019 Available online xxx AMS 2010 codes: 34C15 37D45
a b s t r a c t The paper studies the chaotic synchronization problem of fractional calculus financial system. At the same time, according to the requirements of bank ATM for port security and the security management of mobile storage media, the fractional calculus encryption algorithm is applied to the personal financial data storage medium system. Authorize and manage mobile storage devices to protect against the use risks and security threats caused by mobile storage devices. The research of the thesis shows that the system has certain applicability and can guarantee the security of personal financial data. Simulation examples show the effectiveness of the method. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Fractional calculus Personal financial data storage Media system research Financial data system
1. Introduction China’s self-service equipment has a large number of holdings, and its growth momentum is strong, which plays a prominent role in people’s daily lives. At the end of 2011, the global ATM holding capacity will reach 2 million units, of which China’s ATM reserves will reach 330,0 0 0 units, and the daily processing of cash will exceed 45 billion yuan [1]. Since China’s per capita possession is seriously lower than that of developed countries, and the urban-rural distribution is extremely uneven, there will be a lot of room for ATM growth in China in the next few years, especially in the vast rural areas. At the same time, China’s bank card demand is large. At the end of 2010, the number of bank cards issued in China has reached 2.4 billion, with 1.4 per capita. ATM demand will further increase. In the past five years, the number of selfservice devices has grown at a rate of more than 22% per year. It is estimated that China will have 540,0 0 0 units in 2015. A large number of self-service equipment as an important part of a country’s financial infrastructure has laid an important role in social security and stability. With the development of information technology, U disk and other peripheral mobile storage media have been widely used in ATM maintenance, but in the process of using mobile storage media, such as unauthorized use, internal use, and viruses the
∗
Corresponding author. E-mail address: [email protected] (Y. Yin).
risk of loss or theft of mobile storage media can pose a considerable security risk to ATMs [2]. The theory of fractional calculus operator has been successfully applied in physics, solving many problems in the field of physics. In the past ten years, the fractional calculus theory that has been successfully applied in physics has also been successfully applied in the fields of humanities and social sciences, such as fractional financial models, fractional happiness models, and fractional love models. In view of the above risk problems, we propose a personal financial data mobile storage medium management scheme based on fractional calculus encryption algorithm to realize risk prevention and security management of various mobile storage media [3].
2. Application of fractional calculus in financial system When attending the 2010 Asian Financial Forum, President of the International Monetary Fund, Kahn pointed out that compared with developed countries, the local demand of emerging market economies is more flexible, the economic structure is better, and the unit investment cost is relatively low. Thus, for system (1), we can conservatively assume that c − b − abc0 is one of the characteristics of some emerging market economies. Compared with emerging market economies, the economic structure of developed countries is relatively mature, the elasticity of domestic commodity demand is not high enough, and the unit investment cost is relatively high [4]. Thus, for system (1), we can conservatively
https://doi.org/10.1016/j.chaos.2019.109459 0960-0779/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Y. Yin and L. Wang, Research on personal financial data storage medium system based on fractional order calculus encryption algorithm, Chaos, Solitons and Fractals, https://doi.org/10.1016/j.chaos.2019.109459
ARTICLE IN PRESS
JID: CHAOS 2
[m5G;October 18, 2019;15:17]
Y. Yin and L. Wang / Chaos, Solitons and Fractals xxx (xxxx) xxx
believe that some non-emerging market economies will have the characteristics of c − b − abc ≤ 0. In order to study the fractional form of the system (1), the following Laplace differential form is used: As fractional differential equations appear more and more frequently in engineering applications, effective and simple solution methods for fractional differential equations are becoming more and more important. However, existing methods have various methods. defect. In the following, we introduce a method for solving fractional differential equations based on Laplace transform. This method is simple and intuitive, and is suitable for solving linear fractional differential equations with constant coefficients. 2.1. Laplace transform method Application of Laplace transform method Below we use two examples to illustrate the application of the Laplace transform method. The paper considers the Laplace
transform method to solve the initial value problem of the nonhomogeneous standard fractional differential equations as follows. α y (t ) − λy (t ) = h (t ), (t > 0 )
0 Dt
(1)
[0 Dtα −k y(t )]t=0 = bk , (k = 1, 2, · · · , n ) n−1<α
(2)
Solution: Perform a Laplace transform on both ends of Eq. (1) and use the initial value condition (2) to get:
sα Y (s ) − λY (s ) = H (s ) +
n
bk sk−1
H (s ) Y (s ) = α + s −λ
k=1
(4)
y(t ) =
The Laplace inverse transformation of Eq. (9) gives the solution of the original differential equation as:
y(t ) = b2 t α1 −1 Eα ,α1 (λt α ) + b1 t α −1 Eα ,α (λt α ) t
t 0
(t − τ )α−1 Eα,α (λ(t − τ )α )h(τ )dτ
Among them, α = α1 + α2 . Note: Comparing the above two initial value problems, it is easy to see that they are very similar in form. The only difference is reflected in a standard fractional differential equation based on classical fractional calculus, one based on the sequence fractional calculus. Sequence fractional differential equations, which are different in the initial value. But we found that their solutions are also very similar in expression, the comparison results are as follows:
In the theoretical analysis part of fractional differential equations, we mainly introduce two aspects, one is the nature of the solution of fractional differential equations, and the other is the solution method of fractional differential equations [6]. Since the research on fractional differential equations is not mature enough, the theoretical analysis made is still in the exploratory stage. Most of the existing results are simple extensions of classical calculus equation theory, and can only cover some special forms of fractional differential equations. Much of the existing work is trying to find new theoretical methods to break the existing constraints and strive to construct a complete set of fractional differential equation theory.
Any order integral definition: Let P<0, if f(x) is m+1 order continuous, −p a Dt
f (x ) =
= (5)
Note: The process of solving this problem by iterative method is also given in some literatures. Although the results of the two solutions are the same, it is obvious that the Laplace solution method is more intuitive and simpler. Below we consider the Laplace transform method to solve the initial value problem of the sequence fractional differential equations [5]. α2
(0 Dtα1 y(t )) − λy(t ) = h(t )
[0 Dtα2 −1 (0 Dtα1 y(t ))]t=0 = b1 , [0 Dtα1 −1 y(t )]t=0 = b2
(7)
(8)
p
lim h h→0 nh = t − a
n p r f (t − rh ) r=0
m p+k f (k ) (a )(t − a ) ( p + k + 1 ) k=0 t 1 + (t − τ )−p+m f (m+1) (τ )dτ ( p + k + 1 ) a
(11)
Any order differential definition: Let p>0, if on [a, t], f(k) (t), (k=1,2,...,m+1) is continuous, and m>p-1, for m, the minimum value of p depends on m
f (x ) =
(6)
Perform a Laplace transform on both ends of Eq. (6) and use the initial value condition (7) to get:
(sα1 +α2 − λ )Y (s ) = H (s ) + sα2 b2 − b1
(10)
0
bk t α −k Eα ,α −k+1 (λt α )
0 Dt
(t − τ )α−1 Eα,α (λ(t − τ )α )h(τ )dτ
+
k=1
+
(9)
The Laplace inverse transformation of the formula (3) can obtain the solution of the original differential equation as: n
H (s ) + sα2 b2 + b1 sα2 +α1 − λ
2.2. Grunwald-Letnikow fractional calculus:
k−1
s bk α s −λ
Y (s ) =
(3)
k=1 n
There is:
=
lim fhp (t ) h→0 nh = t − a m −p+k f (k ) (a )(t − a ) (−p + k + 1 ) k=0 t 1 + (t − τ )−p+m f (m+1) (τ )dτ (−p + k + 1 ) a
(12)
Please cite this article as: Y. Yin and L. Wang, Research on personal financial data storage medium system based on fractional order calculus encryption algorithm, Chaos, Solitons and Fractals, https://doi.org/10.1016/j.chaos.2019.109459
JID: CHAOS
ARTICLE IN PRESS
[m5G;October 18, 2019;15:17]
Y. Yin and L. Wang / Chaos, Solitons and Fractals xxx (xxxx) xxx
3. Research and development of fractional calculus personal financial data storage system 3.1. Deployment network diagram Take a provincial branch application as an example. The deployed network architecture is shown in Fig. 1: Following the SOA design concept, the state-owned bank data centralized management system is divided into four system domains: business support, operational support, outreach and management information. The business support system domain includes an acceptance system, a transaction processing system, and an accounting processing system; the operation support system domain includes a common code management system, an operation management system, a monitoring system, and a hot backup and automatic recovery system; the external system domain includes a communication system and an agent. Business interface system, UnionPay system [7]; Management information system domain includes report processing system, historical query system, intelligent decision system and service information system. Each system works together through the application integration platform to support the operation and management of state-owned banks. The overall architecture has the characteristics of “loose coupling, high cohesion”, flexible deployment, stable and reliable, and strong scalability [8]. The system handles intermediate processes such as calculating interest in banking and generating various registration books. The generated accounting information is submitted to the accounting processing system for billing. The accounting is separated from the transaction processing system, which shortens the transaction processing time, avoids resource problems such as excessive transaction processing time due to complex intermediate processes such as interest-bearing in the centralized management system transaction, and improves the processing efficiency of the transaction. The data exchange system functions as an Enterprise Service Bus
3
(ESB). The system uses the loose coupling of message packets to implement information exchange between different services. The management service system provides management services such as system monitoring and fund monitoring. 3.2. Mobile storage media protection (1) System administrator. Municipal branch IT administrator. Filter the USB device usage requirements of ATM maintainers. Create authorizations, distribute authorizations, delete authorizations, and change authorizations for USB licenses. Manage registered devices for USB licenses created: USB loss/deactivation, USB enabled, USB usage statistics. (2) Super administrator. Provincial branch IT administrator. For the management of the System Administrator, configure the number of USB authorization codes and authorization roles that the System Administrator can generate. Management of USB authorization roles: create new roles, delete roles, and modify roles. Manage authorized USB usage: USB loss/deactivation, USB enabled, USB usage statistics. (3) ATM maintenance personnel. USB device user. Authorization registration and use of USB devices. The hierarchical relationship between the roles is shown in Fig. 2. 3.3. Mobile storage media management system Business Management System: Handling services that need to be handled by operators, including manual entry, review, supervision, authorization, group submission, query printing, data import and export, etc., and retain the necessary information. Transaction Processing System: Processing various services submitted by the data exchange system, including control of transaction scheduling, quota, etc., generation of income and expenditure register, processing of transaction information, generation of accounting vouchers, etc. Accounting processing system: Processing
Fig. 1. System network architecture.
Please cite this article as: Y. Yin and L. Wang, Research on personal financial data storage medium system based on fractional order calculus encryption algorithm, Chaos, Solitons and Fractals, https://doi.org/10.1016/j.chaos.2019.109459
ARTICLE IN PRESS
JID: CHAOS 4
[m5G;October 18, 2019;15:17]
Y. Yin and L. Wang / Chaos, Solitons and Fractals xxx (xxxx) xxx
Fig. 2. System administrator and user rights.
billing, inventory, generating receipts, etc. submitted by the data exchange system, batch processing at the beginning and end of the day, responsible for the generation of the running account, the household account, and the general ledger. External communication system: mainly responsible for compiling, generating messages, pledging, decomposing messages, converting message formats, exchanging with other system messages, etc.; running management system: responsible for public parameter code management, operation monitoring, log management, Data management and operator login and sign-off management. Report Processing System: Responsible for collecting and processing data, generating and displaying reports. Historical Query System: Collect and save historical information of the system, such as original vouchers, accounting vouchers, register information, etc. [9]. Data exchange system: Responsible for the communication between the various systems within the data central management system, including receiving the packets sent by each system, performing the necessary processing on the packets, and forwarding the packets to the destination system.
be obtained by substituting partial differential equations:
3.4. Mobile storage media usage process (1) Generate authorization code: According to the needs of ATM maintenance personnel, the bank management personnel can generate the authorization code with the corresponding role authority and aging time through the management background and deliver it to the corresponding personnel. (2) Registration authorization code: ATM maintenance personnel insert the unknown mobile storage device into ATM for the first time, need to register, input legal authorization code and corresponding registration information to complete registration.
4. Financial media system simulation 4.1. Numerical solution - implicit format At present, it is important to study the problem of heat conduction, especially the problem of unsteady heat conduction. The implicit format is used here. Using u(x, t), the forward difference quotient for t: (U kj +1 − U kj )/ t; the second-order center difference for x: +1 +1 (U kj+1 − 2U kj +1 + U kj−1 )/(x )2 .
Implicit
Fig. 3. Numerical solution of the velocity equation of the financial system.
difference
format
can
U jk+1 − U jk t
=
k+1 k+1 U j+1 − 2U jk+1 + U j−1
(x )2
(13)
4.2. Numerical solution - analysis and MATLAB implementation (1) The financial system response time is 2 seconds. The design space step size is h=0.1 and the time step is t=0.01, and the grid ratio is r = t/h2 . Thus, the number of spatial grid points obtained is M1+1, and the number of time grid points is M2 + 1. First set the initial time matrix U (M2 + 1, M1 + 1). The boundary conditions and initial conditions are then written into a matrix representing the running speed distribution. The specific code can be seen in the final appendix (2) Write matrix A. Core code: Diagonal: A (i, j) = 1 + 2r diagonally to the right and below: A (i, i+1) = -r; A (i+1, j) = -r; The following is the use of B to iterate [10]. When k=1, A∗ U (2, j) =U (1, j) When k=2, A∗ U (3, j) =U (2, j) When k=3, A∗ U (4, j) =U (3, j)
Please cite this article as: Y. Yin and L. Wang, Research on personal financial data storage medium system based on fractional order calculus encryption algorithm, Chaos, Solitons and Fractals, https://doi.org/10.1016/j.chaos.2019.109459
JID: CHAOS
ARTICLE IN PRESS
[m5G;October 18, 2019;15:17]
Y. Yin and L. Wang / Chaos, Solitons and Fractals xxx (xxxx) xxx
Fig. 4. Financial data system processing speed graph for numerical solution of smooth transition.
5
Fig. 7. Numerical solution and analytical solution space error (3D map).
Fig. 5. MATLAB running screenshot.
Fig. 8. Numerical solution and analytical solution time error (two-dimensional map).
Fig. 6. Solution processing speed map.
This iteration continues until k=M2 . The distribution matrix U of the processing speed of the banking system over time and space can be obtained. (3) Numerical solution, as shown in Figs. 3 and 4. Now the coloring transitions smoothly. 4.3. Comparison of numerical solutions and analytical solutions Firstly, we need to discretize the analytical solution. There is 2 2 an e−n π t in the analytical solution. When n is getting bigger, it will quickly go to 0, so we can take n=80 0 0. Now to prove the feasibility, the workspace calculation in MATLAB. Draw the running speed distribution of the analytical solution, and numerically draw the drawing, as shown in Fig. 6.
The numerical solution is subtracted from the analytical solution to obtain an error map. As shown in Figs. 7 and 8, we can see the spatial error from Fig. 7, and the error is large at the boundary [11]. We can see the error of time from Fig. 8. At the beginning of the time, the error is the largest, then there is a small fluctuation, and finally the error gradually becomes smaller, and finally it goes to zero [12]. 5. Conclusion Economic chaos is an inherent uncertainty in economic and financial systems. It is an extremely complex phenomenon that often appears in this system and is an important part of current nonlinear economic dynamics research. This paper qualitatively studies the personal financial data storage medium system based on fractional calculus encryption algorithm, and numerically simulates the influence of the savings amount and differential order on the evolution behavior of the fractional financial system complexity, and draws some meaningful results. The research results can provide a theoretical basis for the government to regulate the economic and financial system. In addition, this software implements the software program by using C language programming. The
Please cite this article as: Y. Yin and L. Wang, Research on personal financial data storage medium system based on fractional order calculus encryption algorithm, Chaos, Solitons and Fractals, https://doi.org/10.1016/j.chaos.2019.109459
JID: CHAOS 6
ARTICLE IN PRESS
[m5G;October 18, 2019;15:17]
Y. Yin and L. Wang / Chaos, Solitons and Fractals xxx (xxxx) xxx
software has a wide range of practical engineering prospects through the authorization and management of USB storage devices to prevent the use risks and security threats caused by USB storage devices. Declaration of Competing Interest None. References [1] Smirnov V, Volchenkov D. Five years of phase space dynamics of the standard & poor’s 500. Appl Math Nonlinear Sci 2019;4(1):203–16. [2] González JLR, López JAV, Martínez MF. Raptors “right hunger” characterization to develop sustainable exclusion areas for wildlife at civil & military airports. Appl Math Nonlinear Sci 2018;1(2):335–44. [3] Baskonus HM, Bulut H, Sulaiman TA. New complex hyperbolic structures to the lonngren-wave equation by using sine-gordon expansion method. Appl Math Nonlinear Sci 2019;4(1):141–50. [4] BAGLEY RL. Power law and fractional calculus model of viscoelasticity. AIAA J 1989;27(10):1412–17.
[5] Gutiérrez-Carvajal, de Melo RE, Flávio L, Rosário, Maurício J, Machado, Tenreiro JA. Condition-based diagnosis of mechatronic systems using a fractional calculus approach. Int J Syst Sci 2016;47(9):2169–77. [6] Rahmani Fazli H, Hassani F, Ebadian A, Khajehnasiri AA. National economies in state-space of fractional-order financial system. Afrika Matematika 2016;27(3–4):529–40. [7] Bingsan, Chen, Chunyu, Benjamin, Wilson, Yijian, et al. Fractional modeling and analysis of coupled mr damping system. IEEE/CAA J Automat Sinica 2016;3(3):288–94. [8] TAKAMATSU T, OHMORI H. Online parameter estimation for lithium-ion battery by using adaptive observer for fractional-order system. Electron Commun Japan 2017;137(8):1015–23. [9] Tirandaz H, Karami-Mollaee A. On active synchronization of fractional-order bloch chaotic system and its practical application in secure image transmission. Int J Intell ComputCybern 2018;11(2):181–96. [10] Liang, Gui-shu J, Yong-ming L, Zong-en, Liu X, Ma L. Modelling of frequency characteristics of the oil-paper compound insulation based on the fractional calculus. Iet Sci Measur Technol 2017;11(5):646–54. [11] Huang C, Duan JS. Steady-state response to periodic excitation in fractional vibration system. J Mech 2016;32(1):25–33. [12] Kaslik, Eva. Analysis of two- and three-dimensional fractional-order hindmarsh-rose type neuronal models. Fract Calculus Appl Anal 2017;20(3):623–45.
Please cite this article as: Y. Yin and L. Wang, Research on personal financial data storage medium system based on fractional order calculus encryption algorithm, Chaos, Solitons and Fractals, https://doi.org/10.1016/j.chaos.2019.109459