Optimal polynomial stability of the Timoshenko system with single fractional boundary dissipation

Reem Alrebdi; Ahmed Bchatnia; Saleh Fahad Aljurbua; Reem Alrebdi; Ahmed Bchatnia; Saleh Fahad Aljurbua

doi:10.3934/math.2025654

AIMS Mathematics

2025, Volume 10, Issue 6: 14515-14538. doi: 10.3934/math.2025654

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Optimal polynomial stability of the Timoshenko system with single fractional boundary dissipation

1.
Department of Mathematics, College of Science, Qassim University, Saudi Arabia
2.
Department of Mathematics, Faculty of Sciences of Tunis, LR Analyse Non-Linéaire et Géométrie, LR21ES08, University of Tunis El Manar, Tunis, 2092, Tunisia

Received: 22 March 2025 Revised: 15 June 2025 Accepted: 23 June 2025 Published: 26 June 2025
MSC : 34A08, 47D03, 93B52, 34K35

This study investigates Timoshenko systems with a single boundary condition involving fractional dissipation. Utilizing semigroup theory, we establish the existence and uniqueness of solutions. Our findings indicate that although the system demonstrates strong stability, it does not attain uniform stability. As a result, we derive the optimal polynomial decay rate of the system.
- fractional derivatives,
- differential equations,
- fractional differential equations,
- Timoshenko systems,
- semi-group
Citation: Reem Alrebdi, Ahmed Bchatnia, Saleh Fahad Aljurbua. Optimal polynomial stability of the Timoshenko system with single fractional boundary dissipation[J]. AIMS Mathematics, 2025, 10(6): 14515-14538. doi: 10.3934/math.2025654

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Abstract

This study investigates Timoshenko systems with a single boundary condition involving fractional dissipation. Utilizing semigroup theory, we establish the existence and uniqueness of solutions. Our findings indicate that although the system demonstrates strong stability, it does not attain uniform stability. As a result, we derive the optimal polynomial decay rate of the system.

References

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