Analytic Study on Hilfer Fractional Langevin Equations with Impulses

Abstract

In this paper, we find a solution of a new type of Langevin equation involving Hilfer fractional derivatives with impulsive effect. We formulate sufficient conditions for the existence and uniqueness of solutions. Moreover, we present Hyers-Ulam stability results. Mathematics Subject Classification: 26A33, 34K40, 34K14.