Sufficient Conditions for Ulam–Hyers–Rassias Stability of Fractional-Order Hopfield Neural Networks

Ding Yali and Bai Nan

Journal of Mathematics, 2026, vol. 2026, 1-9

Abstract: In this paper, we study the Ulam–Hyers–Rassias stability of fractional-order Hopfield neural networks (FHNNs). By using the Mittag-Leffler function and Gronwall’s inequality, we show that such FHNNs are Ulam–Hyers–Rassias stable when the neuron activation functions satisfy the Lipschitz condition. This work provides two sufficient conditions for the Ulam–Hyers–Rassias and Ulam–Hyers stability of neural networks, based on the self-feedback coefficient matrix and the connection weight matrix. Finally, numerical simulation experiments are carried out with appropriate network coefficients satisfying the given theorem, which verify the correctness of the obtained results.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:1647573

DOI: 10.1155/jom/1647573

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