Positive solution for a class of singular semipositone fractional differential equations with integral boundary conditions

Xingqiu Zhang

doi:10.1186/1687-2770-2012-123

Abstract

In this article, by employing a fixed point theorem in cones, we investigate the existence of a positive solution for a class of singular semipositone fractional differential equations with integral boundary conditions. We also obtain some relations between the solution and Green's function. MSC: 26A33; 34B15; 34B16; 34G20

Highlights

We consider the existence of a positive solution for the following singular semipositone fractional differential equations:
We present Green’s function of the fractional differential equation boundary value problem
Lemma . (Fixed point theorem of cone expansion and compression of norm type [ ]) Let and be two bounded open sets in a Banach space E such that θ ∈ and ⊂

Summary

Introduction

We consider the existence of a positive solution for the following singular semipositone fractional differential equations: Much attention has been attached to the existence of positive solutions for semipositone differential equations and the system of differential equations; see [ – ] and references therein to name a few. Webb obtained sharp results on the existence of positive solutions under a suitable condition on f . In two recent papers [ ] and [ ], by means of the fixed point theory and fixed point index theory, the authors investigated the existence and multiplicity of positive solutions for the following two kinds of fractional differential equations with integral boundary value problems:

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Conclusion