Nonlocal Coupled System for (k,φ)-Hilfer Fractional Differential Equations

Abstract

In this paper, we study a coupled system consisting of (k,φ)-Hilfer fractional differential equations of the order (1,2], supplemented with nonlocal coupled multi-point boundary conditions. The existence and uniqueness of the results are established via Banach’s contraction mapping principle, the Leray–Schauder alternative and Krasnosel’skiĭ’s fixed-point theorem. Numerical examples are constructed to illustrate the obtained results.