Abstract and Applied Analysis

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

I. J. Cabrera, J. Harjani, and K. B. Sadarangani

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Abstract

We investigate the existence and uniqueness of positive solutions for the following singular fractional three-point boundary value problem D 0 + α u ( t ) + f ( t , u ( t ) ) = 0, 0 < t < 1 , u ( 0 ) = u ( 0 ) = u ′′ ( 0 ) = 0 , u ′′ ( 1 ) = β u ′′ ( η ) , where 3 < α 4 , D 0 + α is the standard Riemann-Liouville derivative and f : ( 0,1 ] × [ 0 , ) [ 0 , ) with lim t 0 + f ( t , · ) = (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

Permanent link to this document
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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