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Research Article | Open Access

A fractional Halanay inequality for neutral systems and its application to Cohen-Grossberg neural networks

Department of Basic Engineering Sciences, College of Engineering, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 34151, Saudi Arabia
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Abstract

We expand the Halanay inequality to accommodate fractional-order systems incorporating both discrete and distributed neutral delays. By establishing specific conditions, we demonstrate that the solutions of these systems converge to zero at a Mittag-Leffler rate. Our analysis is versatile, accommodating a wide range of delay kernels. This versatility extends the applicability of our findings to fractional Cohen-Grossberg neural networks, offering valuable insights into their stability and dynamical behavior.

Keywords

Halanay inequalityCohen-Grossberg neural network systemCaputo fractional derivativeneutral delayMittag-Leffler stability
CLC number: 92B20, 26A33, 34D20

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AIMS Mathematics
Volume 10 Issue 2,
February 2025
Pages 2466-2491
DOI: 10.3934/math.2025115

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Cite this article:
Kassim MD. A fractional Halanay inequality for neutral systems and its application to Cohen-Grossberg neural networks. AIMS Mathematics, 2025, 10(2): 2466-2491. https://doi.org/10.3934/math.2025115

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Received: 31 December 2024
Revised: 26 January 2025
Accepted: 08 February 2025
Published: 15 February 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)