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.

arXiv comment13 pages

References in corpus (5)

• Stability of $\psi$-Hilfer Impulsive Fractional Differential Equations
• Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems
• On the existence and stability for non-instantaneuos impulsive fractional integrodifferential equation
• Combined Fractional Variational Problems of Variable Order and Some Computational Aspects
• A Fractional Gauss-Jacobi quadrature rule for approximating fractional integrals and derivatives

Cited by in corpus (1)

• Nonlocal Boundary Value Problem for Generalized Hilfer Implicit Fractional Differential Equations