Asymptotical stability for fractional-order Hopfield neural networks with multiple time delays

This paper is concerned with the asymptotical stability of fractional-order Hopfield neural networks with multiple delays. The problem is actually a generalization of stability for linear fractional-order delayed differential equations: (Formula presented.), which is widely studied when (Formula presented.). However, the stability is rarely known when (Formula presented.). Hence, this work is mainly devoted to the stability analysis for (Formula presented.). By virtue of the Laplace transform method and a decoupling technique for the characteristic equation, we propose a necessary and sufficient condition to ensure the stability, which improves the existing stability results for (Formula presented.). Afterward, by a linearization technique, a necessary and sufficient stability condition is also presented for fractional-order Hopfield neural networks with multiple delays. The conditions are established by delay-independent coefficient-type criteria. Finally, several numerical simulations are given to show the effectiveness of our results.