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

Lamya Almaghamsi; Aeshah Alghamdi; Abdeljabbar Ghanmi; Lamya Almaghamsi; Aeshah Alghamdi; Abdeljabbar Ghanmi

doi:10.3934/math.2025024

AIMS Mathematics

2025, Volume 10, Issue 1: 534-550. doi: 10.3934/math.2025024

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

1.
Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah 21493, Saudi Arabia
2.
ENIT-LAMSIN, BP. 37, 1002 Tunis-Belv$\acute{{\rm{d}}}\grave{{\rm{r}}}$e, Tunis El Manar university, Tunis, Tunisia

Received: 19 October 2024 Revised: 12 December 2024 Accepted: 03 January 2025 Published: 10 January 2025
MSC : 26A33, 34A08, 35J20

This study examines the existence of a solution for a nonvariational Langevin equation that involves the $ \psi $-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.
- variational methods,
- fractional calculus,
- Langevin equation,
- generalized Riemann Liouville operators
Citation: Lamya Almaghamsi, Aeshah Alghamdi, Abdeljabbar Ghanmi. Existence of solution for a Langevin equation involving the $ \psi $-Hilfer fractional derivative: A variational approach[J]. AIMS Mathematics, 2025, 10(1): 534-550. doi: 10.3934/math.2025024

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Abstract

This study examines the existence of a solution for a nonvariational Langevin equation that involves the $ \psi $-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.

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