Uniqueness and existence of positive solutions for a multi-point boundary value problem of singular fractional differential equations

Wen-Xue Zhou,Yan-Dong Chu,Dumitru Băleanu

doi:10.1186/1687-1847-2013-114

Abstract

In this paper, we study the uniqueness of a positive solution for the singular nonlinear fractional differential equation boundary value problem , , , , where is a real number, is the standard Riemann-Liouville differentiation and , with . Our analysis relies on a fixed-point theorem in partially ordered set. As an application, an example is presented to illustrate the main result. MSC:26A33, 34B15, 34K37.

Highlights

Fractional differential equations have gained considerable importance due to their application in various sciences, such as physics, mechanics, chemistry, engineering, etc
Qiu and Bai [ ] considered the existence of a positive solution to boundary value problems of the nonlinear fractional differential equation cDα +u(t) + f t, u(t) =, < t
Motivated by all the works above, this paper is mainly concerned with the uniqueness of a positive solution for the singular nonlinear fractional differential equation boundary value problem

Summary

Introduction

Fractional differential equations have gained considerable importance due to their application in various sciences, such as physics, mechanics, chemistry, engineering, etc. There are few papers, which have considered the singular boundary value problems of fractional differential equations; see [ – ]. Delbosco and Rodino [ ] considered the existence of a solution for the nonlinear fractional differential equation Dα +u = f (t, u), where < α < and f : [ , a] × R → R, < a ≤ +∞ is a given continuous function in ( , a) × R.

Results

Conclusion