Positive solutions for singular nonlinear fractional differential equation with integral boundary conditions

Hongdan Li,Lishan Liu,Yonghong Wu

doi:10.1186/s13661-015-0493-3

Abstract

In this article, we study the existence of positive solutions for a class of singular nonlinear fractional differential equations with Riemann-Stieltjes integral boundary conditions. Using the properties of the Green function and the fixed point theory in cones, we obtain some results on the existence of positive solutions. Our results extend and improve many known results including singular and nonsingular cases.

Highlights

1 Introduction In this article, we consider the existence of solutions for the following class of singular fractional differential equations:
Motivated by the above-mentioned papers, the purpose of this article is to investigate the existence of positive solutions for the more general fractional differential equations
We develop some properties of the Green function

Summary

Introduction

1 Introduction In this article, we consider the existence of solutions for the following class of singular fractional differential equations: Cabada and Hamdi [ ] studied the existence of positive solutions of the following nonlinear fractional differential equation with integral boundary value conditions: Dα + u(t) + f (t, u(t)) = , < t < , u( ) = u ( ) = , u( ) = λ ds, where < α ≤ , < λ, λ = α, Dα + is the Riemann-Liouville fractional derivative, and f : [ , ] × [ , ∞) → [ , ∞) is a continuous function. By means of the monotone iteration method, Sun and Zhao [ ] investigated the existence of positive solutions for the fractional differential equation with integral boundary conditions

Objectives

Results

Conclusion