On a class of non-local boundary value problem for a $\psi$-Hilfer non-linear fractional integro-differential equation

Abstract

In this paper, the existence, uniqueness, and stability of the solution of $\psi$-Hilfer non-linear fractional integro-differential equation with mixed boundary conditions are investigated. The existence and uniqueness are shown by Krasnosel'skii's fixed point theorem and Banach contraction principle under a special working space. Furthermore, the Ulam-Hyers-Rassias stability and semi Ulam-Hyers-Rassias stability of the solution are analysed. An example is given to illustrate the main results.