Synchronization and Anti-synchronization between a Class of Fractional-order and Integer-order Chaotic Systems with Only One Controller Term

In order to bridge between fractional-order and integer order nonlinear dynamical system, in this letter, we brings attention to synchronization and anti-synchronization between fractional-order chaotic system and integer-order chaotic system by using back-stepping method. And the sufficient conditions for achieving the synchronization and anti-synchronization of a class of fractional-order nonlinear system and integerorder nonlinear system are derived based on Lyapunov stability theory. Moreover, a new back-stepping control law with only one term is introduced such that a typical example can be realized successfully, which is easier to be applied to industry for its only one controller term. Finally, numerical simulations are provided to verify the effectiveness and feasibility of the proposed control scheme, which are in agreement with theoretical analysis.