Abstract
Chaos theory deals with the behavior of dynamical systems that are highly sensitive to initial conditions. Chaotic systems are characterized by the property that small changes in the initial conditions result in widely diverging responses. In this paper, new control schemes of synchronization for different arbitrary incommensurate and commensurate fractional order chaotic systems are presented. Synchronization stability, based on stability of linear fractional-order systems and fractional Lyapunov stability, is proved theoretically. Numerical examples are given to show the effectiveness of the proposed method.