Mittag-Leffler stability and stabilization of delayed fractional-order memristive neural networks based on a new Razumikhin-type theorem

The Mittag-Leffler stability and stabilization of delayed fractional -order memristive neural networks(DFMNNs) are investigated in this paper. First, two new fractional Halanay inequalities are established by solving two fractional -order non -autonomous differential inequalities. Next, by using the proposed fractional Halanay inequalities, a novel Razumikhin-type theorem for Mittag-Leffler stability of delayed fractional -order systems is presented, which is an extension of the so-called Razumikhin theorem for integer -order delayed differential systems. Applying the Razumikhin-type theorem to the DFMNNs, several Mittag-Leffler stability and stabilization criteria are obtained. Finally, the validity of the proposed results is shown by two numerical examples.