Numerical Solutions of a Variable-Order Fractional Financial System
The numerical solution of a variable-order fractional financial system is calculated by using the Adams-Bashforth-Moulton method. The derivative is defined in the Caputo variable-order fractional sense. Numerical examples show that the Adams-Bashforth-Moulton method can be applied to solve such vari...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/417942 |
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| author | Shichang Ma Yufeng Xu Wei Yue |
| author_facet | Shichang Ma Yufeng Xu Wei Yue |
| author_sort | Shichang Ma |
| collection | DOAJ |
| description | The numerical solution of a variable-order fractional financial system is calculated by using the Adams-Bashforth-Moulton method. The derivative is defined in the Caputo variable-order fractional sense. Numerical examples show that the Adams-Bashforth-Moulton method can be applied to solve such variable-order fractional differential equations simply and effectively. The convergent order of the method is also estimated numerically. Moreover, the stable equilibrium point, quasiperiodic trajectory, and chaotic attractor are found in the variable-order fractional financial system with proper order functions. |
| format | Article |
| id | doaj-art-c99656b81ab6429ebc9f4ee59d470f11 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-c99656b81ab6429ebc9f4ee59d470f112025-02-03T06:14:15ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/417942417942Numerical Solutions of a Variable-Order Fractional Financial SystemShichang Ma0Yufeng Xu1Wei Yue2School of Business, Central South University, Hunan, Changsha 410083, ChinaDepartment of Applied Mathematics, Central South University, Hunan, Changsha 410083, ChinaSchool of Business, Central South University, Hunan, Changsha 410083, ChinaThe numerical solution of a variable-order fractional financial system is calculated by using the Adams-Bashforth-Moulton method. The derivative is defined in the Caputo variable-order fractional sense. Numerical examples show that the Adams-Bashforth-Moulton method can be applied to solve such variable-order fractional differential equations simply and effectively. The convergent order of the method is also estimated numerically. Moreover, the stable equilibrium point, quasiperiodic trajectory, and chaotic attractor are found in the variable-order fractional financial system with proper order functions.http://dx.doi.org/10.1155/2012/417942 |
| spellingShingle | Shichang Ma Yufeng Xu Wei Yue Numerical Solutions of a Variable-Order Fractional Financial System Journal of Applied Mathematics |
| title | Numerical Solutions of a Variable-Order Fractional Financial System |
| title_full | Numerical Solutions of a Variable-Order Fractional Financial System |
| title_fullStr | Numerical Solutions of a Variable-Order Fractional Financial System |
| title_full_unstemmed | Numerical Solutions of a Variable-Order Fractional Financial System |
| title_short | Numerical Solutions of a Variable-Order Fractional Financial System |
| title_sort | numerical solutions of a variable order fractional financial system |
| url | http://dx.doi.org/10.1155/2012/417942 |
| work_keys_str_mv | AT shichangma numericalsolutionsofavariableorderfractionalfinancialsystem AT yufengxu numericalsolutionsofavariableorderfractionalfinancialsystem AT weiyue numericalsolutionsofavariableorderfractionalfinancialsystem |