A fully Hadamard and Erdélyi–Kober-type integral boundary value problem of a coupled system of implicit differential equations

Abstract

In this article, we give sufficient conditions for the existence of solutions for a new coupled system of secondorderimplicit differential equations with Hadamard and Erdélyi–Kober fractional integral boundary conditions andnonlocal conditions at the boundaries in Banach space. The main result is based on a Mönch fixed point theoremcombined with the measure of noncompactness of Kuratowski; an example is given to illustrate our approach.