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2012 Existence and Uniqueness of Positive Solutions for a Singular Fractional Three-Point Boundary Value Problem
I. J. Cabrera, J. Harjani, K. B. Sadarangani
Abstr. Appl. Anal. 2012(SI01): 1-18 (2012). DOI: 10.1155/2012/803417

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.

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I. J. Cabrera. J. Harjani. K. B. Sadarangani. "Existence and Uniqueness of Positive Solutions for a Singular Fractional Three-Point Boundary Value Problem." Abstr. Appl. Anal. 2012 (SI01) 1 - 18, 2012. https://doi.org/10.1155/2012/803417

Information

Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1246.34006
MathSciNet: MR2965441
Digital Object Identifier: 10.1155/2012/803417

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI01 • 2012
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