Asymptotical stability and synchronization of Riemann–Liouville fractional delayed neural networks

In this paper, we investigate the asymptotical stability and synchronization of fractional neural networks. Multiple time-varying delays and distributed delays are taken into consideration simultaneously. First, by applying the Banach’s fixed point theorem, the existence and uniqueness of fractional delayed neural networks are proposed. Then, to guarantee the asymptotical stability of the demonstrated system, two sufficient conditions are derived by integral-order Lyapunov direct method. Furthermore, two synchronization criteria are presented based on the adaptive controller. The above results significantly generalize the existed conclusions in the previous works. At last, numerical simulations are taken to check the validity and feasibility of the achieved methods.