Investigation of a Nonlinear Coupled (<i>k</i>, <i>ψ</i>)–Hilfer Fractional Differential System with Coupled (<i>k</i>, <i>ψ</i>)–Riemann–Liouville Fractional Integral Boundary Conditions

Abstract

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

Keywords

• (<i>k</i>,<i>ψ</i>)–Hilfer fractional derivative
• nonlinear systems of equations
• (<i>k</i>,<i>ψ</i>)–Riemann–Liouville fractional integral boundary conditions
• existence of solutions
• fixed point