## Abstract and Applied Analysis

### Positive Solutions for Multipoint Boundary Value Problem of Fractional Differential Equations

Wenyong Zhong

#### Abstract

We study the existence and multiplicity of positive solutions for the fractional $m$-point boundary value problem ${D}_{0+}^{\alpha }u(t)+f(t,u(t))=0$, $0\lt t\lt 1$, $u(0)=u\text{'}(0)=0$, $u\text{'}(1)={\sum }_{i=1}^{m-2}{a}_{i}u\text{'}({\xi }_{i})$, where $2\lt \alpha \lt 3$, ${D}_{0+}^{\alpha }$ is the standard Riemann-Liouville fractional derivative, and $f:[0,1]\times [0,\infty)\mapsto [0,\infty)$ is continuous. Here, ${a}_{i}\geq 0$ for $i=1,\dots ,m-2$, $0\lt {\xi }_{1}\lt {\xi }_{2}\lt \cdots \lt {\xi }_{m-2}\lt 1$, and $\rho ={\sum }_{i=1}^{m-2}{a}_{i}{\xi }_{i}^{\alpha -2}$ with $\rho \lt 1$. In light of some fixed point theorems, some existence and multiplicity results of positive solutions are obtained.

#### Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 601492, 15 pages.

Dates
First available in Project Euclid: 12 August 2011

https://projecteuclid.org/euclid.aaa/1313170935

Digital Object Identifier
doi:10.1155/2010/601492

Mathematical Reviews number (MathSciNet)
MR2746013

Zentralblatt MATH identifier
1223.34008

#### Citation

Zhong, Wenyong. Positive Solutions for Multipoint Boundary Value Problem of Fractional Differential Equations. Abstr. Appl. Anal. 2010 (2010), Article ID 601492, 15 pages. doi:10.1155/2010/601492. https://projecteuclid.org/euclid.aaa/1313170935