An infinite number of nonnegative solutions for iterative system of singular fractional order boundary value problems

Abstract

In this paper, we consider the iterative system of singular Rimean-Liouville fractional order boundary value problems with RiemannStieltjes integral boundary conditions involving increasing homeomorphism and positive homomorphism operator(IHPHO). By using Krasnoselskii’s cone fixed point theorem in a Banach space, we derive sufficent conditions for the existence of infinite number of nonnegative solutions. The sufficient conditions are also derived for the existence of unique nonnegative solution to the addressed problem by fixed point theorem in a complete metric space. As an application, we present an example to illustrate the main results.