On Implicit $\psi$-Caputo Fractional Integro-differential Equations

TL;DR

This paper studies the existence, uniqueness, and qualitative properties of solutions to nonlinear $\psi$-Caputo fractional integro-differential equations using fixed point theorems and inequalities.

Contribution

It provides new results on solution existence, uniqueness, and stability for $\psi$-Caputo fractional equations, expanding the theoretical understanding of such equations.

Findings

Proved existence and uniqueness of solutions.

Derived stability and estimate results.

Applied fixed point theorem and Gronwall inequality.

Abstract

In this paper, we investigate the existence and uniqueness of solution of nonlinear $\psi$-Caputo fractional differential equation with the help of Banach fixed point theorem. Moreover, by using $\psi$-Gronwall inequality, we studied some qualitative properties of solutions such as estimate and stability.