## Abstract and Applied Analysis

### Existence and Uniqueness of Positive Solutions for a Singular Fractional Three-Point Boundary Value Problem

#### Abstract

We investigate the existence and uniqueness of positive solutions for the following singular fractional three-point boundary value problem ${D}_{{0}^{+}}^{\alpha }u(t)+f(t,u(t))=0, 0, where $3<\alpha \le 4$, ${D}_{{0}^{+}}^{\alpha }$ is the standard Riemann-Liouville derivative and $f:(0,1]{\times}[0,\infty )\to [0,\infty )$ with ${\mathrm{lim} }_{t\to {0}^{+}}f(t,·)=\infty$ (i.e., $f$ is singular at $t=0$). Our analysis relies on a fixed point theorem in partially ordered metric spaces.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 803417, 18 pages.

Dates
First available in Project Euclid: 5 April 2013

https://projecteuclid.org/euclid.aaa/1365168354

Digital Object Identifier
doi:10.1155/2012/803417

Mathematical Reviews number (MathSciNet)
MR2965441

Zentralblatt MATH identifier
1246.34006

#### Citation

Cabrera, I. J.; Harjani, J.; Sadarangani, K. B. Existence and Uniqueness of Positive Solutions for a Singular Fractional Three-Point Boundary Value Problem. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 803417, 18 pages. doi:10.1155/2012/803417. https://projecteuclid.org/euclid.aaa/1365168354

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