Synchronization of chaotic fractional-order systems via active sliding mode controller

In this paper, we propose a controller based on active sliding mode theory to synchronize chaotic fractional-order systems in master–slave structure. Master and slave systems may be identical or different. Based on stability theorems in the fractional calculus, analysis of stability is performed for the proposed method. Finally, three numerical simulations (synchronizing fractional-order Lü–Lü systems, synchronizing fractional order Chen–Chen systems and synchronizing fractional-order Lü–Chen systems) are presented to show the effectiveness of the proposed controller. The simulations are implemented using two different numerical methods to solve the fractional differential equations.