Stability of the fractional Volterra integro‐differential equation by means of ψ‐Hilfer operator

Abstract

In this paper, using the Riemann‐Liouville fractional integral with respect to another function and the ψ−Hilfer fractional derivative, we propose a fractional Volterra integral equation and the fractional Volterra integro‐differential equation. In this sense, for this new fractional Volterra integro‐differential equation, we study the Ulam‐Hyers stability and, also, the fractional Volterra integral equation in the Banach space, by means of the Banach fixed‐point theorem. As an application, we present the Ulam‐Hyers stability using the α‐resolvent operator in the Sobolev space .