Existence and stability results for a coupled system of Hilfer fractional Langevin equation with non local integral boundary value conditions

Abstract

This paper deals with the existence and uniqueness of solution for a coupled system of Hilfer fractional Langevin equation with non local integral boundary value conditions. The novelty of this work is that it is more general than the works based on the derivative of Caputo and Riemann-Liouville, because when $\beta =0$ we find the Riemann-Liouville fractional derivative and when $\beta =1$ we find the Caputo fractional derivative. Initially, we give some definitions and notions that will be used throughout the work, after that we will establish the existence and uniqueness results by employing the fixed point theorems. Finaly, we investigate different kinds of stability such as Ulam-Hyers stability, generalized Ulam-Hyers stability.