An innfite number of nonnegative solutions for iterative system of singular fractional order Boundary value problems

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