Solvability of a Class of Coupled Implicit Fractional Langevin Differential Equations by the Laplace transform

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.