Kapula Prasad - Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, ۵۳۰۰۰۳-India.
Khuddush Mahammad - Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, ۵۳۰۰۰۳-India.
Veeraiah Pogadadanda - Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, ۵۳۰۰۰۳-India.

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 Krasnoselskii’s cone fixed point theorem in a Banach space, we derive sufficient conditions for the existence of an infinite number of nonnegative solutions. The sufficient conditions are also derived for the existence of a unique nonnegative solution to the addressed problem by fixed point theorem in complete metric space. As an application, we present an example to illustrate the main results.

Iterative system, Riemann-Stieltjes integral, homeomorphism, nonegative solutions