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Research Article | Open Access

Existence of solution for a Langevin equation involving the ψ-Hilfer fractional derivative: A variational approach

Lamya Almaghamsi1( ), Aeshah Alghamdi1, Abdeljabbar Ghanmi2
Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 21493, Saudi Arabia
ENIT-LAMSIN, BP. 37, 1002 Tunis-Belvd´r`e, Tunis El Manar university, Tunis, Tunisia
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Abstract

This study examines the existence of a solution for a nonvariational Langevin equation that involves the ψ-Hilfer fractional derivative. More specifically, we apply the mountain pass theorem, and then an iterative approach to establish the existence of a solution for the problem.

Keywords

variational methodsfractional calculusLangevin equationgeneralized Riemann Liouville operators
CLC number: 26A33, 34A08, 35J20

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AIMS Mathematics
Volume 10 Issue 1,
January 2025
Pages 534-550
DOI: 10.3934/math.2025024

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Cite this article:
Almaghamsi L, Alghamdi A, Ghanmi A. Existence of solution for a Langevin equation involving the ψ-Hilfer fractional derivative: A variational approach. AIMS Mathematics, 2025, 10(1): 534-550. https://doi.org/10.3934/math.2025024

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Received: 19 October 2024
Revised: 12 December 2024
Accepted: 03 January 2025
Published: 15 January 2025
©2025 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)