Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control

• Projective cluster synchronization of the fractional complex network is studied.
• An efficient method is proposed for discussing synchronization of delayed fractional complex networks.
• A first order adaptive pinning controller is designed.

This paper investigates the projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control. The pinning control method is employed in designing controllers for guaranteeing projective cluster synchronization. Based on the Lyapunov stability theory and well-known Barbalat’s lemma, some new sufficient conditions are derived to guarantee the projective cluster synchronization of the fractional-order complex network. A numerical simulation is given to verify the effectiveness of the theoretical results.