SOLVABILITY OF LANGEVIN FRACTIONAL DIFFERENTIAL EQUATION OF HIGHER-ORDER WITH INTEGRAL BOUNDARY CONDITIONS

Abdelati El Allaoui; Lamine Mbarki; Youssef Allaoui; J. Vanterler da C. Sousa

doi:10.11948/20240092

2025 Volume 15 Issue 1

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Abdelati El Allaoui, Lamine Mbarki, Youssef Allaoui, J. Vanterler da C. Sousa. SOLVABILITY OF LANGEVIN FRACTIONAL DIFFERENTIAL EQUATION OF HIGHER-ORDER WITH INTEGRAL BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 316-332. doi: 10.11948/20240092

Citation:

Abdelati El Allaoui, Lamine Mbarki, Youssef Allaoui, J. Vanterler da C. Sousa. SOLVABILITY OF LANGEVIN FRACTIONAL DIFFERENTIAL EQUATION OF HIGHER-ORDER WITH INTEGRAL BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 316-332. doi: 10.11948/20240092

SOLVABILITY OF LANGEVIN FRACTIONAL DIFFERENTIAL EQUATION OF HIGHER-ORDER WITH INTEGRAL BOUNDARY CONDITIONS

1.
MISCOM, National School of Applied Sciences, Cadi Ayyad University, Safi, Morocco
2.
Department of Mathematics, Faculty of Sciences, University of Tunis El Manar, Tunisia
3.
LMACS, Faculty of Sciences and Technics, Sultan Moulay Slimane University, Béni MEllal, Morocco
4.
Aerospace Engineering, PPGEA-UEMA, Department of Mathematics, DEMATI-UEMA, São Luís, MA 65054, Brazil

Author Bio: Email: a.elallaoui@uca.ma(A. E. Allaoui); Email: mbarki.lamine2016@gmail.com(L. Mbarki); Email: youssefallaoui@usms.ma(Y. Allaoui)
Corresponding author: Email: vanterler@ime.unicamp.br(J. Vanterler da C. Sousa)

Abstract

Abstract

This paper we concern the solvability and uniqueness of higher-order Langevin fractional differential equations subject to integral boundary conditions. We establish the existence of solutions using Krasnoselskii's fixed point theorem, while uniqueness is demonstrated through the application of the Banach fixed point theorem. The obtained results offer insights into the solution space of these complex differential equations, shedding light on their behavior and properties. To illustrate the practical implications of our findings, we provide a concrete example at the end of this paper.
- Caputo fractional derivative /
- boundary conditions /
- fractional differential equation
MSC: 34A08, 34A12

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