New finite-time and global Mittag-Leffler stability criteria for fractional-order inertial Cohen–Grossberg neural networks with S-type distributed delays

Wei Liu; Danning Xu; Qiuyang Zhang; Huawen Liu; Tao Jiang; Hui Pan; Wei Liu; Danning Xu; Qiuyang Zhang; Huawen Liu; Tao Jiang; Hui Pan

doi:10.3934/math.2026849

AIMS Mathematics

2026, Volume 11, Issue 7: 20915-20929. doi: 10.3934/math.2026849

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Research article

New finite-time and global Mittag-Leffler stability criteria for fractional-order inertial Cohen–Grossberg neural networks with S-type distributed delays

1.
School of Artificial Intelligence, Shaoxing Institute of Technology, Qunxian Middle Rd. 2799, Shaoxing 312000, China
2.
School of Mathematical Sciences, Zhejiang University, Yuhangtang Rd. 866, Hangzhou 310058, China

Received: 29 March 2026 Revised: 09 June 2026 Accepted: 18 June 2026 Published: 15 July 2026
MSC : 34K20, 92B20

This paper studied the finite-time stability (FTS) and global Mittag-Leffler stability (GMLS) of a class of fractional inertial Cohen-Grossberg neural networks (FICGNNs) with S-type distributed delays. A unified modeling framework based on Lebesgue-Stieltjes integrals was adopted to encompass both discrete and continuously distributed delays. By establishing transformation between the fractional-order integrals of the state function with and without S-type distributed delays, new criteria for the corresponding FTS and GMLS were rigorously derived under appropriate assumptions. The theoretical results were further verified through numerical simulations.
- fractional-order,
- S-type distributed delays,
- Cohen-Grossberg neural networks,
- finite-time stability,
- global Mittag-Leffler stability
Citation: Wei Liu, Danning Xu, Qiuyang Zhang, Huawen Liu, Tao Jiang, Hui Pan. New finite-time and global Mittag-Leffler stability criteria for fractional-order inertial Cohen–Grossberg neural networks with S-type distributed delays[J]. AIMS Mathematics, 2026, 11(7): 20915-20929. doi: 10.3934/math.2026849

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Abstract

This paper studied the finite-time stability (FTS) and global Mittag-Leffler stability (GMLS) of a class of fractional inertial Cohen-Grossberg neural networks (FICGNNs) with S-type distributed delays. A unified modeling framework based on Lebesgue-Stieltjes integrals was adopted to encompass both discrete and continuously distributed delays. By establishing transformation between the fractional-order integrals of the state function with and without S-type distributed delays, new criteria for the corresponding FTS and GMLS were rigorously derived under appropriate assumptions. The theoretical results were further verified through numerical simulations.

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