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Research Article | Open Access

Fractional Timoshenko beam with a viscoelastically damped rotational component

Banan Al-Homidan1, Nasser-eddine Tatar2( )
Imam Abdulrahman bin Faisal University, Department of Mathematics, College of Sciences, P. O. Box 1982, Dammam, Saudi Arabia
King Fahd University of Petroleum and Minerals, Department of Mathematics, Interdisciplinary Research Center for Intelligent Manufacturing and Robotics, Dhahran 31261, Saudi Arabia
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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.

Keywords

Caputo fractional derivativeRiemann-Liouville fractional derivativeMittag-Leffler stabilityLyapunov stabilitymultiplier technique
CLC number: 26A33, 35B35, 35B40, 35L20

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AIMS Mathematics
Volume 8 Issue 10,
October 2023
Pages 24632-24662
DOI: 10.3934/math.20231256

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Al-Homidan B, Tatar N-e. Fractional Timoshenko beam with a viscoelastically damped rotational component. AIMS Mathematics, 2023, 8(10): 24632-24662. https://doi.org/10.3934/math.20231256

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Received: 13 April 2023
Revised: 24 June 2023
Accepted: 02 July 2023
Published: 15 October 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)