Study on a Nonlocal Fractional Coupled System Involving (<i>k</i>,<i>ψ</i>)-Hilfer Derivatives and (<i>k</i>,<i>ψ</i>)-Riemann–Liouville Integral Operators

Abstract

This paper deals with a nonlocal fractional coupled system of (k,ψ)-Hilfer fractional differential equations, which involve, in boundary conditions, (k,ψ)-Hilfer fractional derivatives and (k,ψ)-Riemann–Liouville fractional integrals. The existence and uniqueness of solutions are established for the considered coupled system by using standard tools from fixed point theory. More precisely, Banach and Krasnosel’skiĭ’s fixed-point theorems are used, along with Leray–Schauder alternative. The obtained results are illustrated by constructed numerical examples.

Keywords

• Hilfer fractional differential system
• fractional integrals
• nonlocal boundary conditions
• existence and uniqueness
• fixed-point theorems