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 [0, T], equipped with nonlinear ψ-Riemann-Liouville fractional integral boundary conditions of different orders 0 < α, β < 1, we deal with a recently introduced ψ-Caputo fractional derivative of order 1 < q ≤ 2. 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. ARTICLE HISTORY

In this research work, we investigate the existence of solutions for a class of nonlinear boundary value problems for fractional-order differential inclusion with respect to another function. Endpoint theorem for [Formula: see text]-weak contractive maps is the main tool in determining our results. An example is presented in aim to illustrate the results.

This note is concerned with establishing the existence of solutions to a fractional differential inclusion of a ψ-Caputo-type with a nonlocal integral boundary condition. Using the concept of the endpoint theorem for φ-weak contractive maps, we investigate the existence of solutions to the proposed problem. An example is provided at the end to clarify the theoretical result.

This research article is mainly concerned with the existence of solutions for a coupled Caputo–Hadamard of nonconvex fractional differential inclusions equipped with boundary conditions. We derive our main result by applying Mizoguchi–Takahashi’s fixed point theorem with the help of $\mathcal{P}$ P -function characterizations.