Stability analysis of nonlinear implicit fractional Langevin equation with noninstantaneous impulses

Abstract

Abstract In this paper, we consider a nonlocal boundary value problem of nonlinear implicit fractional Langevin equation with noninstantaneous impulses. We study the existence, uniqueness and generalized Ulam–Hyers–Rassias stability of the proposed model with the help of fixed point approach, over generalized complete metric space. We give an example which supports our main result.

Keywords

• Implicit Langevin equation
• Caputo derivative
• noninstantaneous impulses
• Ulam–Hyers–Rassias stability