Projective synchronization for fractional-order memristor-based neural networks with time delays

In this paper, the global projective synchronization for fractional-order memristor-based neural networks with multiple time delays is investigated via combining open loop control with the time-delayed feedback control. A comparison theorem for a class of fractional-order systems with multiple time delays is proposed. Based on the given comparison theorem and Lyapunov method, the synchronization conditions are derived under the framework of Filippov solution and differential inclusion theory. Several feedback control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization for the fractional-order memristor-based neural networks with time delays. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.