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Research Article | Open Access

Fractional derivative boundary control in coupled Euler-Bernoulli beams: stability and discrete energy decay

Boumediene Boukhari1, Foued Mtiri2, Ahmed Bchatnia3( ), Abderrahmane Beniani1
Department of Mathematics, Faculty of Science and Technology, Engineering and Sustainable Development Laboratory, University of Ain Temouchent, Ain Témouchent, 46000, Algeria
Department of Mathematics, Applied College in Mahayil, King Khalid University, Abha, Saudi Arabia
Department of Mathematics, Faculty of Sciences of Tunis, LR Analyse Non-Linéaire et Géométrie, LR21ES08, University of Tunis El Manar, Tunis, 2092, Tunisia
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Abstract

This paper analyzes an Euler-Bernoulli beam equation in a bounded domain with a boundary control condition involving a fractional derivative. By utilizing the semigroup theory of linear operators and building on the results of Borichev and Tomilov, the stability properties of the system are examined. Additionally, a numerical scheme is developed to reproduce various decay rate behaviors. The numerical simulations confirm the theoretical stability results regarding the energy decay rate and demonstrate exponential decay for specific configurations of initial data.

Keywords

Euler-Bernoulli beam equationdynamic boundary dissipation of fractional derivative typefrequency domain methodstrong stability
CLC number: 26A33, 35L55, 74D05, 93D15, 93D20

References

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AIMS Mathematics
Volume 9 Issue 11,
November 2024
Pages 32102-32123
DOI: 10.3934/math.20241541

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Boukhari B, Mtiri F, Bchatnia A, et al. Fractional derivative boundary control in coupled Euler-Bernoulli beams: stability and discrete energy decay. AIMS Mathematics, 2024, 9(11): 32102-32123. https://doi.org/10.3934/math.20241541

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Received: 06 September 2024
Revised: 30 October 2024
Accepted: 30 October 2024
Published: 12 November 2024
©2024 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)