Stability analysis of fractional-order Hopfield neural networks with time delays

•Stability of fractional-order time delay neural networks with hub structures is analyzed.•Fractional-order neural networks with ring structures and time delays are developed.•Stability conditions of the developed fractional-order neural networks are obtained.•The influence of time delays on the stability is discussed.

This paper investigates the stability for fractional-order Hopfield neural networks with time delays. Firstly, the fractional-order Hopfield neural networks with hub structure and time delays are studied. Some sufficient conditions for stability of the systems are obtained. Next, two fractional-order Hopfield neural networks with different ring structures and time delays are developed. By studying the developed neural networks, the corresponding sufficient conditions for stability of the systems are also derived. It is shown that the stability conditions are independent of time delays. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results obtained in this paper.