Topological Degree Method for a Class of Ψ-Caputo Fractional Differential Langevin Equation

This paper deals with the existence and uniqueness of solution for a new class of Ψ-Caputo fractional differential Langevin equation. The suggested study is based on some basic definitions of topological degree theory and fractional calculus. We established the existence result by using the topological degree method for condensing maps, and by means of Banach’s fixed point theorem we obtained the uniqueness result. As application, we give an illustrative example to demonstrate our theoretical result.