Synchronization of fractional-order reaction-diffusion neural networks via mixed boundary control

This article studies the synchronization issue of fractional reaction-diffusion neural networks (FRDNNs) with time delay and mixed boundary condition. First, a novel boundary controller with constant-valued gain is designed, which only relies on the boundary state information. Subsequently, by virtue of Lyapunov direct technique and LMI approach, the Mittag–Leffler synchronization conditions are established. Besides, to effectively regulate the control gain, a fractional-order adaptive boundary controller is developed and the adaptive synchronization of FRDNNs is rigorously analyzed. Note that, the above control strategies are also workable for traditional integer-order reaction-diffusion neural networks. The developed theoretical analysis is supported eventually via a numerical example.