Numerical Solutions of a Variable-Order Fractional Financial System

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: Shichang Ma, Yufeng Xu, Wei Yue
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/417942
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spelling doaj-c99656b81ab6429ebc9f4ee59d470f112020-11-24T22:38:01ZengHindawi LimitedJournal 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
collection DOAJ
language English
format Article
sources DOAJ
author Shichang Ma
Yufeng Xu
Wei Yue
spellingShingle Shichang Ma
Yufeng Xu
Wei Yue
Numerical Solutions of a Variable-Order Fractional Financial System
Journal of Applied Mathematics
author_facet Shichang Ma
Yufeng Xu
Wei Yue
author_sort Shichang Ma
title Numerical Solutions of a Variable-Order Fractional Financial System
title_short 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_sort numerical solutions of a variable-order fractional financial system
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
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.
url http://dx.doi.org/10.1155/2012/417942
work_keys_str_mv AT shichangma numericalsolutionsofavariableorderfractionalfinancialsystem
AT yufengxu numericalsolutionsofavariableorderfractionalfinancialsystem
AT weiyue numericalsolutionsofavariableorderfractionalfinancialsystem
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