Synchronization analysis of fractional-order inertial-type neural networks with time delays

This paper is dedicated to the global Mittag-Leffler synchronization (GMLS) of fractional-order inertial-type neural networks (FOITNNs) with time delays. To begin with, based on the semigroup property of the Caputo fractional derivative (CFD), an appropriate variable substitution is chosen to transform the original fractional-order inertial system into a traditional fractional -order system. Secondly, two types of discontinuous control schemes with delays and only a control input are proposed: one is the state feedback control and the other is the fractional-order adaptive control. On the basis of Lyapunov stability theory and fractional-order differential inequalities, some new sufficient criteria for the GMLS of two FOITNNs are established. Furthermore, the control gains here can be selected more widely, which makes the results more applicative and less conservative. Finally, two numerical examples validate the efficacy of the obtained results.(c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.