## Abstract and Applied Analysis

### Positive Solutions for Boundary Value Problems of Singular Fractional Differential Equations

#### Abstract

In this paper, by using a fixed point theorem, we investigate the existence of a positive solution to the singular fractional boundary value problem ${D_{C}}_{0+}^{\alpha }u+f(t,u,{D_{C}}_{0+}^{\nu }u,{D_{C}}_{0+}^{\mu }u)+g(t,u,{D_{C}}_{0+}^{\nu }u,{D_{C}}_{0+}^{\mu }u)=0$, $u(0)={u}^{\prime }(0)={u}^{\prime \prime }(0)={u}^{\prime \prime \prime }(0)=0$, where $3<\alpha <4$, $0<\nu <1$, $1<\mu <2$, ${D_{C}}_{0+}^{\alpha }$ is Caputo fractional derivative, $f(t,x,y,z)$ is singular at the value 0 of its arguments $x,y,z$, and $g(t,x,y,z)$ satisfies the Lipschitz condition.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 129640, 7 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393443526

Digital Object Identifier
doi:10.1155/2013/129640

Mathematical Reviews number (MathSciNet)
MR3064542

Zentralblatt MATH identifier
1307.34005

#### Citation

Bai, Zhanbing; Sun, Weichen; Zhang, Weihai. Positive Solutions for Boundary Value Problems of Singular Fractional Differential Equations. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 129640, 7 pages. doi:10.1155/2013/129640. https://projecteuclid.org/euclid.aaa/1393443526

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