Solvability of a class of coupled implicit fractional Langevin differential equations by the Laplace transform

Asmaa Baihi; Ayoub Louakar; Hamid Lmou; Mohamed  El Fadouaki; Ahmed Kajouni; Khalid Hilal

doi:10.5269/bspm.76849

Asmaa Baihi
Ayoub Louakar
Hamid Lmou Laboratory of Applied Mathematics and Scientific Competing, Faculty of Sciences and Technics, Sultan Moulay Slimane University, Beni Mellal, Morocco.
Mohamed El Fadouaki
Ahmed Kajouni
Khalid Hilal

Abstract

This article is devoted to establishing the existence and unicity of the coupled implicit fractional Langevin differential equation with initial conditions, using Laplace transform method. At first, we obtained the existence and uniqueness results using the Banach contraction principle. Second, the existence result was obtained by applying Schaefer’s fixed point theorem. To support our main results, we present an example.

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