Document Type : Research Paper

**Authors**

Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, 530003-India.

**Abstract**

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.

**Keywords**

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October 2021

Pages 940-958

**Receive Date:**02 August 2020**Revise Date:**25 November 2020**Accept Date:**06 December 2020