On a Nonlocal Coupled System of Hilfer Generalized Proportional Fractional Differential Equations

This paper studies the existence and uniqueness of solutions for a coupled system of Hilfer-type generalized proportional fractional differential equations supplemented with nonlocal asymmetric multipoint boundary conditions. We consider both the scalar and the Banach space case. We apply standard fixed-point theorems to derive the desired results. In the scalar case, we apply Banach's fixed-point theorem, the Leray-Schauder alternative, and Krasnosel'skii's fixed-point theorem. The Banach space case is based on Monch's fixed-point theorem and the technique of the measure of noncompactness. Examples illustrating the main results are presented. Symmetric distance between itself and its derivative can be investigated by replacing the proportional number equal to one half.