A generalized version of Halanay inequality applied to a fractional nonlinear Hopfield neural network system

Abstract The standard Halanay inequality is generalized by considering fractional derivatives instead of first-order derivatives and also the nonlinear case. Moreover, we shall deal with a large class of kernels in distributed delays. It is then used to prove the Mittag-Leffler stability of a fractional nonlinear Hopfield neural network system with activation functions that are not necessarily Lipschitz continuous. The findings are supported by two explicit classes of admissible kernels and an example.