Nonlinear generalized fractional differential equations with generalized fractional integral conditions

Abstract

This research work is dedicated to an investigation of the existence and uniqueness of a class of nonlinear ψ-Caputo fractional differential equation on a finite interval , equipped with nonlinear ψ-Riemann–Liouville fractional integral boundary conditions of different orders , we deal with a recently introduced ψ-Caputo fractional derivative of order . The formulated problem will be transformed into an integral equation with the help of Green function. A full analysis of existence and uniqueness of solutions is proved using fixed point theorems: Leray–Schauder nonlinear alternative, Krasnoselskii and Schauder's fixed point theorems, Banach's and Boyd–Wong's contraction principles. We show that this class generalizes several other existing classes of fractional-order differential equations, and therefore the freedom of choice of the standard fractional operator. As an application, we provide an example to demonstrate the validity of our results.