Synchronization analysis for fractional non-autonomous neural networks by a Halanay inequality

In this paper, based on the asymptotic expansion of Mittag-Leffler function and the fractional comparison principle, an improved fractional Halanay inequality with time-varying coefficients is proved by introducing parameters λi and δ. The fractional autonomous Halanay inequality is generalized to the fractional non-autonomous case. Moreover, based on the improved fractional Halanay inequality and Lyapunov functional method, a novel sufficient condition on self synchronization of the fractional non-autonomous Hopfield neural networks with time delay is obtained. Finally, three numerical examples are given to demonstrate the effectiveness of proposed methods.