On the Generalized Hilfer Fractional Coupled Integro-Differential Systems with Multi-Point Ordinary and Fractional Integral Boundary Conditions

Abstract

In this paper, we investigate a nonlinear coupled integro-differential system involving generalized Hilfer fractional derivative operators ((k,ψ)-Hilfer type) of different orders and equipped with non-local multi-point ordinary and fractional integral boundary conditions. The uniqueness results for the given problem are obtained by applying Banach’s contraction mapping principle and the Boyd–Wong fixed point theorem for nonlinear contractions. Based on the Laray–Schauder alternative and the well-known fixed-point theorem due to Krasnosel’skiĭ, the existence of solutions for the problem at hand is established under different criteria. Illustrative examples for the main results are constructed.

Keywords

• (<i>k</i>,<i>ψ</i>)-Hilfer fractional derivative
• fractional differential system
• existence
• uniqueness
• fixed point theorems