Existence, uniqueness and Ulam's stabilities for a class of implicit impulsive Langevin equation with Hilfer fractional derivatives

Abstract

In this manuscript, a class of implicit impulsive Langevin equation with Hilfer fractional derivatives is considered. Using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss existence, uniqueness, Ulam-Hyers, generalized Ulam-Hyers, Ulam-Hyers-Rassias and generalized Ulam-Hyers-Rassias stability results of our proposed model, with the help of Banach's fixed point theorem. An example is provided at the end to illustrate our results.

Keywords

• langevin equation
• hilfer fractional derivative
• instantaneous impulses
• ulam-hyers-rassias stability