Existence and stability of a nonlinear fractional differential equation involving a $\psi$-Caputo operator

Year 2020, Volume: 4 Issue: 4, 266 - 278, 30.12.2020

Hanan A. Wahash , Mohammed Abdo , Satish K. Panchal

https://doi.org/10.31197/atnaa.664534

Cited By: 8

Abstract

This paper is devoted to the study of the existence and interval of existence, uniqueness of solutions and estimates on solutions of the nonlocal Cauchy problem for nonlinear fractional differential equations involving a Caputo type fractional derivative with respect to another function $\psi$. Further, we prove four different types of Ulam stability results of solutions for a given problem. The tools used in this article are the classical technique of Banach fixed point theorem and generalized Gronwall inequality. At the end, illustrative examples are presented.

Keywords

fractional differential equations, Existence and stability, Fixed point theorem, ψ-fractional derivative and ψ-fractional integral

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