Qualitative study of a new class of coupled pantograph differential equations involving the psi-Hilfer fractional derivative with multi-point boundary conditions

Abstract

In this paper, we study the existence and uniqueness of solutions of a coupled system of $\psi$-Hilfer fractional pantograph differential equations with multi-point boundary conditions. The existence and uniqueness results are given by using the fixed point theorems, mainly, Banach's contraction principle and Krasnoselskii's fixed point theorem. Finally, two examples are provided to illustrate the results.