Investigation of a Nonlinear Coupled (k, ?)–Hilfer Fractional Differential System with Coupled (k, ?)–Riemann–Liouville Fractional Integral Boundary Conditions

This paper is concerned with the existence of solutions for a new boundary value problem nonlinear coupled (k,?)–Hilfer fractional differential equations subject to (k,?)–Riemann–Liouville integral conditions. We prove two results by applying Leray–Schauder alternative, and Krasnosel’ski?’s fixed-point theorem under different criteria, while third result, concerning uniqueness given problem, relies on Banach’s contraction mapping principle. Examples are included illustrating abstract results.