Existence and nonexistence of positive solutions for fractional integral boundary value problem with two disturbance parameters

Xiao Wang,Xiping Liu,Xuejing Deng

doi:10.1186/s13661-015-0450-1

Abstract

In this paper, we consider a class of fractional differential equations with integral boundary conditions which involve two disturbance parameters. By using the Guo-Krasnoselskii fixed point theorem, new results on the existence and nonexistence of positive solutions for the boundary value problem are obtained. And the impact of the disturbance parameters on the existence of positive solutions is also investigated. Finally, we give some examples to illustrate our main results.

Highlights

1 Introduction The theory of boundary value problems for ordinary differential equations and functional differential equations plays an important role in many research fields of science and engineering; for details, see [ – ] and the references therein
Fractional differential equations have widely appeared in various fields such as physics, mechanics, electricity, biology, control theory, etc
X = x(t) is a solution of the integral equation ( . ) if it is the solution of the boundary value problem ( . )-( . ), and vice versa

Summary

Introduction

The theory of boundary value problems for ordinary differential equations and functional differential equations plays an important role in many research fields of science and engineering; for details, see [ – ] and the references therein. As an important part of fractional differential equations, the integral boundary value problems have been extensively researched, see [ – ]. The existence and nonexistence of positive solutions for the integral boundary value problem

Results

Conclusion