Journal of Applied Mathematics
Volume 2012 (2012), Article ID 417942, 14 pages
http://dx.doi.org/10.1155/2012/417942
Research Article

Numerical Solutions of a Variable-Order Fractional Financial System

Shichang Ma,1 Yufeng Xu,2 and Wei Yue1

1School of Business, Central South University, Hunan, Changsha 410083, China
2Department of Applied Mathematics, Central South University, Hunan, Changsha 410083, China

Received 10 May 2012; Revised 21 July 2012; Accepted 6 August 2012

Academic Editor: Changbum Chun

Copyright © 2012 Shichang Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.