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.