Nonlinear fractional distributed Halanay inequality and application to neural network systems

The standard first order distributed Halanay inequality is generalized in more than one direction. We prove a fractional nonlinear version of this inequality for a large class of kernels which are not necessarily exponentially decaying to zero. This result is used to prove Mittag-Leffler stability of a Hopfiled neural network system with not necessarily globally Lipschitz continuous activation functions. Two classes of important admissible kernels and an example are provided to illustrate our findings. (c) 2021 Elsevier Ltd. All rights reserved.