Green's function for singular fractional differential equations and applications

03/20/2022

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by   Jinsil Lee, et al.

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University of Georgia

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Pusan National University

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In this paper, we study the existence of positive solutions for nonlinear fractional differential equations with a singular weight. We derive Green's function and corresponding integral operator and then examine the compactness of the operator. As an application, we prove an existence-result for positive solutions when a nonlinear term satisfies either superlinear or sublinear conditions. The proof was mainly employed by Krasnoselski's classical fixed point theorem.