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

Muhammad Fahim Aslam; Jianghao Hao; Salah Boulaaras; Luqman Bashir; Muhammad Fahim Aslam; Jianghao Hao; Salah Boulaaras; Luqman Bashir

doi:10.3934/era.2025199

Electronic Research Archive

2025, Volume 33, Issue 7: 4363-4381. doi: 10.3934/era.2025199

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Research article

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

1.
School of Mathematics and Statistics, Shanxi University, Taiyuan 030006, China
2.
Department of Mathematics, University of Kotli Azad Jammu and Kashmir (UOKAJK), Kotli, Pakistan
3.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

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

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.
- plate equation,
- general decay,
- fractional derivatives,
- infinite memory,
- global existence,
- nonlinear equations
Citation: Muhammad Fahim Aslam, Jianghao Hao, Salah Boulaaras, Luqman Bashir. Global existence and exponential stability of a fractionally damped plate equation with past history[J]. Electronic Research Archive, 2025, 33(7): 4363-4381. doi: 10.3934/era.2025199

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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.

References

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