Fractional Timoshenko beam with a viscoelastically damped rotational component

Banan Al-Homidan; Nasser-eddine Tatar; Banan Al-Homidan; Nasser-eddine Tatar

doi:10.3934/math.20231256

AIMS Mathematics

2023, Volume 8, Issue 10: 24632-24662. doi: 10.3934/math.20231256

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Research article

Fractional Timoshenko beam with a viscoelastically damped rotational component

Banan Al-Homidan ¹,
Nasser-eddine Tatar ^{2
,
,}

1.
Imam Abdulrahman bin Faisal University, Department of Mathematics, College of Sciences, P. O. Box 1982, Dammam, Saudi Arabia
2.
King Fahd University of Petroleum and Minerals, Department of Mathematics, Interdisciplinary Research Center for Intelligent Manufacturing and Robotics, Dhahran 31261, Saudi Arabia

Received: 13 April 2023 Revised: 24 June 2023 Accepted: 02 July 2023 Published: 21 August 2023
MSC : 26A33, 35B35, 35B40, 35L20

This paper is concerned with a fractional Timoshenko system of order between one and two. We address the question of well-posedness in an appropriate space when the rotational component is viscoelastic or subject to a viscoelastic controller. To this end we use the notion of alpha-resolvent. Moreover, we prove that the memory term alone may stabilize the system in a Mittag-Leffler fashion. The system is Lyapunov stable or uniformly stable in the case of different speeds of propagation.
- Caputo fractional derivative,
- Riemann-Liouville fractional derivative,
- Mittag-Leffler stability,
- Lyapunov stability,
- multiplier technique
Citation: Banan Al-Homidan, Nasser-eddine Tatar. Fractional Timoshenko beam with a viscoelastically damped rotational component[J]. AIMS Mathematics, 2023, 8(10): 24632-24662. doi: 10.3934/math.20231256

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Abstract

This paper is concerned with a fractional Timoshenko system of order between one and two. We address the question of well-posedness in an appropriate space when the rotational component is viscoelastic or subject to a viscoelastic controller. To this end we use the notion of alpha-resolvent. Moreover, we prove that the memory term alone may stabilize the system in a Mittag-Leffler fashion. The system is Lyapunov stable or uniformly stable in the case of different speeds of propagation.

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