International Journal of Differential Equations
Volume 2011 (2011), Article ID 635165, 12 pages
http://dx.doi.org/10.1155/2011/635165
Research Article

Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative

Fengrong Zhang,1,2 Changpin Li,1 and YangQuan Chen3

1Department of Mathematics, Shanghai University, Shanghai 200444, China
2School of Mathematics and Computational Science, China University of Petroleum (East China), Qingdao 266555, China
3Electrical and Computer Engineering Department, Utah State University, Logan, UT 84322-4160, USA

Received 18 April 2011; Accepted 14 June 2011

Academic Editor: Fawang Liu

Copyright © 2011 Fengrong Zhang 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

This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.