Global Mittag-Leffler synchronization for neural networks modeled by impulsive caputo fractional differential equations with distributed delays

Abstract

The synchronization problem for impulsive fractional-order neural networks with both time-varying bounded and distributed delays is studied. We study the case when the neural networks and the fractional derivatives of all neurons depend significantly on the moments of impulses and we consider both the cases of state coupling controllers and output coupling controllers. The fractional generalization of the Razumikhin method and Lyapunov functions is applied. Initially, a brief overview of the basic fractional derivatives of Lyapunov functions used in the literature is given. Some sufficient conditions are derived to realize the global Mittag-Leffler synchronization of impulsive fractional-order neural networks. Our results are illustrated with examples.