## Abstract and Applied Analysis

### The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications

#### Abstract

We consider the properties of Green’s function for the nonlinear fractional differential equation boundary value problem: ${\mathbf{D}}_{0+}^{\alpha }u(t)+f(t,u(t))+e(t)=0,0, where $n-1<\alpha \le n,n\ge 3,0<\beta \le 1,0\le \eta \le 1$, ${\mathbf{D}}_{0+}^{\alpha }$ is the standard Riemann-Liouville derivative. Here our nonlinearity $f$ may be singular at $u=0$. As applications of Green’s function, we give some multiple positive solutions for singular boundary value problems by means of Schauder fixed-point theorem.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 531038, 12 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393450200

Digital Object Identifier
doi:10.1155/2013/531038

Mathematical Reviews number (MathSciNet)
MR3034993

Zentralblatt MATH identifier
1274.34062

#### Citation

Jiang, Fuquan; Xu, Xiaojie; Cao, Zhongwei. The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 531038, 12 pages. doi:10.1155/2013/531038. https://projecteuclid.org/euclid.aaa/1393450200

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