Stability and pinning synchronization of delayed memristive neural networks with fractional-order and reaction–diffusion terms

Global asymptotic stability and synchronization are explored in this paper for fractional delayed memristive neural networks with reaction–diffusion terms (FDRDMNNs) in sense of Riemann–Liouville. First, we introduce diffusion into the existing model of fractional delayed memristive neural networks. Next, in terms of Green's theorem and inequality technique, a less conservative criterion for the asymptotic stability of FDRDMNNs is given by endowing Lyapunov direct method. Then, the appropriate pinning feedback controllers and adaptive controllers are designed to achieve the synchronization of the FDRDMNNs, and two sufficient conditions for global asymptotic synchronization are acquired. In addition, the results based on algebraic inequalities enhance some existing ones. The numerical simulations finally verify the validity of the derived results.