Mean-square stability of Riemann–Liouville fractional Hopfield’s graded response neural networks with random impulses

Abstract In this paper a model of Hopfield’s graded response neural network is investigated. A whose neurons are subject to certain impulsive state displacement at random times considered. The set up and studied. presence moments impulses in the leads change solutions stochastic processes. Also, we use Riemann–Liouville fractional derivative adequately long-term memory nonlocality networks. We an appropriate way both initial conditions moments. application new definition equilibrium point. define mean-square Mittag-Leffler stability time point study type stability. Some sufficient for obtained. general case with varying self-regulating parameters all units functions connection between two