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Research Article | Open Access

Energy decay for a porous system with a fractional operator in the memory

Chahrazed Messikh1, Soraya Labidi1, Ahmed Bchatnia2( ), Foued Mtiri3
Department of Mathematics, Applied Mathematics Laboratory, Badji Mokhtar University, Annaba 23000, Algeria
LR Analyse Non-Linéaire et Géométrie, LR21ES08, Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El Manar, Tunisia
Department of Mathematics, Applied College in Mahayil, King Khalid University, Abha 61421, Saudi Arabia
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Abstract

In this work, we examine a porous-elastic system with a fractional operator incorporated in the memory term, which acts exclusively on one equation within the system. Under appropriate conditions on the polynomially decreasing kernels of the memory type, we establish the result of polynomial decay.

Keywords

porous systempolynomial decaymemory termrelaxation function

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Electronic Research Archive
Volume 33 Issue 4,
April 2025
Pages 2195-2215
DOI: 10.3934/era.2025096

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Cite this article:
Messikh C, Labidi S, Bchatnia A, et al. Energy decay for a porous system with a fractional operator in the memory. Electronic Research Archive, 2025, 33(4): 2195-2215. https://doi.org/10.3934/era.2025096

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Received: 30 December 2024
Revised: 07 April 2025
Accepted: 09 April 2025
Published: 15 April 2025
©2025 the Author(s), licensee AIMS Press.

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