Existence Theory and Stability Analysis of Fractional Langevin Equation

Abstract

Abstract In this paper, we consider a non local boundary value problem of nonlinear fractional Langevin equation with non-instantaneous impulses. Initially, we form a standard framework to originate a formula of solutions to our proposed model and then implement the concept of generalized Ulam–Hyers–Rassias using Diaz–Margolis’s fixed point theorem over a generalized complete metric space.