Green's function for singular fractional differential equations and applications

TL;DR

This paper develops Green's functions for singular fractional differential equations, establishing existence results for positive solutions using fixed point theorems, with applications to nonlinear equations under superlinear or sublinear conditions.

Contribution

It introduces a Green's function approach for singular fractional differential equations and applies fixed point theorems to prove existence of positive solutions.

Findings

Green's function derived for singular fractional equations

Existence of positive solutions proved under superlinear/sublinear conditions

Application of Krasnoselski's fixed point theorem to nonlinear problems

Abstract

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.