On the Ulam-Hyers stabilities of Ψ-Hilfer fractional differential equation by means of abstract Volterra operator

Abstract: In this paper, we consider the new class of the fractional differential equation involving the abstract Volterra operator in the Banach space and investigate existence, uniqueness and stabilities of Ulam--Hyers on the compact interval $\Delta=[a,b]$ and on the infinite interval $I=[a,\infty )$. Our analysis is based on the application of the Banach fixed point theorem and the Gronwall inequality involving generalized $\Psi$-fractional integral. At last, we performed out an application to elucidate the outcomes got.