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Research Article | Open Access

Global existence and energy decay for a transmission problem under a boundary fractional derivative type

Noureddine Bahri1,2, Abderrahmane Beniani3, Abdelkader Braik1,4, Svetlin G. Georgiev5, Zayd Hajjej6, Khaled Zennir7( )
Faculty of Science and Technology, Hasiba Benbouali University, Chlef 02000-Algeria
Laboratory of Mathematics and Applications, Hassib Benbouali University, Chlef 02000, Algeria
Department of Mathematics, University Ain Tmouchent, Belhadj Bouchaib, B.P. 284 RP, Ain Temouchent 46000, Algeria
Laboratory of Fundamental and Applicable Mathematics of Oran, University of Oran1 Ahmed Ben Bella, B.P. 1524 El M'naouar, Oran 31000, Algeria
Department of Mathematics, Sorbonne University, 75005, Paris, France
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945 Guelma. B.P. 401 Guelma 24000 Algérie
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Abstract

The paper considers the effects of fractional derivative with a high degree of accuracy in the boundary conditions for the transmission problem. It is shown that the existence and uniqueness of the solutions for the transmission problem in a bounded domain with a boundary condition given by a fractional term in the second equation are guaranteed by using the semigroup theory. Under an appropriate assumptions on the transmission conditions and boundary conditions, we also discuss the exponential and strong stability of solution by also introducing the theory of semigroups.

Keywords

fractional derivativeswave equationtransmission problemdelay termexponential stability
CLC number: 35B37, 35L55, 74D05, 93D15, 93D20

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AIMS Mathematics
Volume 8 Issue 11,
November 2023
Pages 27605-27625
DOI: 10.3934/math.20231412

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Cite this article:
Bahri N, Beniani A, Braik A, et al. Global existence and energy decay for a transmission problem under a boundary fractional derivative type. AIMS Mathematics, 2023, 8(11): 27605-27625. https://doi.org/10.3934/math.20231412

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Received: 10 June 2023
Revised: 16 September 2023
Accepted: 20 September 2023
Published: 15 November 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)