The stability of the fractional Volterra integro-differential equation by means of Ψ-Hilfer operator revisited

Abstract

In this note, we have as main purpose to investigate the Ulam-Hyers stability of a fractional Volterra integral equation through the Banach fixed point theorem and present an example on Ulam-Hyers stability using operator theory α-resolvent in order to elucidate the investigated result. Our results modify the Theorem 4 of Sousa and et. al. [Sousa JVC, Rodrigues FG, Oliveira EC. Stability of the fractional Volterra integro-differential equation by means of Ψ-Hilfer operator. Math Meth Appl Sci. 2019;42(9):3033-3043.] and present a corrected proof with a modified approximation.