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Research Article | Open Access

Global existence and exponential stability of a fractionally damped plate equation with past history

Muhammad Fahim Aslam1,2( ), Jianghao Hao1, Salah Boulaaras3, Luqman Bashir1
School of Mathematics and Statistics, Shanxi University, Taiyuan 030006, China
Department of Mathematics, University of Kotli Azad Jammu and Kashmir (UOKAJK), Kotli, Pakistan
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
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Abstract

This paper is an extension of our earlier research[1]. In this article, we discussed the fractionally damped plate equation with infinite memory. We proved that solutions are global under different initial and boundary conditions. Subsequently, we investigated the exponential stability of the solutions through Lyapunov functionals in order to establish stability conditions sufficient for stability analysis.

Keywords

plate equationgeneral decayfractional derivativesinfinite memoryglobal existencenonlinear equations

References

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Electronic Research Archive
Volume 33 Issue 7,
July 2025
Pages 4363-4381
DOI: 10.3934/era.2025199

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Cite this article:
Aslam MF, Hao J, Boulaaras S, et al. Global existence and exponential stability of a fractionally damped plate equation with past history. Electronic Research Archive, 2025, 33(7): 4363-4381. https://doi.org/10.3934/era.2025199

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Received: 29 April 2025
Revised: 09 July 2025
Accepted: 21 July 2025
Published: 30 July 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)