Polynomial Decay of the Energy of Solutions of the Timoshenko System with Two Boundary Fractional Dissipations-Reference-Cited by-同舟云学术

Polynomial Decay of the Energy of Solutions of the Timoshenko System with Two Boundary Fractional Dissipations

Published:2024-08-28 Issue:9 Volume:8 Page:507
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Alfalqi Suleman¹^ORCID,Khiar Hamid²^ORCID,Bchatnia Ahmed³^ORCID,Beniani Abderrahmane²^ORCID

Affiliation:

1. Department of Mathematics, Applied College in Mahayil, King Khalid University, Abha 61421, Saudi Arabia

2. Engineering and Sustainable Development Laboratory, Faculty of Science and Technology, University of Ain Temouchent, Ain Temouchent 46000, Algeria

3. LR Analyse Non-Linéaire et Géométrie, LR21ES08, Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El Manar, Tunis 2092, Tunisia

Abstract

In this study, we examine Timoshenko systems with boundary conditions featuring two types of fractional dissipations. By applying semigroup theory, we demonstrate the existence and uniqueness of solutions. Our analysis shows that while the system exhibits strong stability, it does not achieve uniform stability. Consequently, we derive a polynomial decay rate for the system.

Publisher

MDPI AG

Link

https://www.mdpi.com/2504-3110/8/9/507/pdf

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