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 Hilfer-type generalized proportional fractional differential equations supplemented with nonlocal asymmetric multipoint boundary conditions. We consider both scalar Banach space case. apply standard fixed-point theorems to derive desired results. In case, we Banach’s theorem, Leray–Schauder alternative, Krasnosel’ski?’s theorem. The case is based on Mönch’s theorem technique measure noncompactness. Examples illustrating main results are presented. Symmetric distance between itself its derivative can be investigated by replacing number equal one half.