Existence and Stability Results for Fractional Langevin Equation in Complex Domain

Abstract

One generalization of the Langevin equation for systems in fractal media replaces the ordinary derivative with a fractional derivative, providing a more accurate description of dynamics in complex environments. In this paper,
we examine a boundary value problem using a Langevin equation with two real fractional orders. The operators are taken in Srivastava-Owa sense in the unit disk. The existence of solutions in a Banach space is established using the contraction mapping concept and Krasnoselskii’s fixed point theorem. Moreover, Ulam Hyers stability for the fractional Langevin equation(FLE) is introduced in this study.