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Advances in Mathematical Physics
Volume 2018 (2018), Article ID 3545083, 9 pages
https://doi.org/10.1155/2018/3545083
Research Article

Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems

College of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, China

Correspondence should be addressed to Chenhui Wang; nc.ude.tumx@gnawhc

Received 5 October 2017; Revised 19 December 2017; Accepted 20 December 2017; Published 17 January 2018

Academic Editor: Christos Volos

Copyright © 2018 Chenhui Wang. 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

Some sufficient conditions, which are valid for stability check of fractional-order nonlinear systems, are given in this paper. Based on these results, the synchronization of two fractional-order chaotic systems is investigated. A novel fractional-order sliding surface, which is composed of a synchronization error and its fractional-order integral, is introduced. The asymptotical stability of the synchronization error dynamical system can be guaranteed by the proposed fractional-order sliding mode controller. Finally, two numerical examples are given to show the feasibility of the proposed methods.