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Title: On existence and uniqueness of positive solutions to a class of fractional boundary value problems
Authors: Caballero, J. 
Harjani, Jackie 
Sadarangani Sadarangani, Kishin B. 
UNESCO Clasification: 1202 Análisis y análisis funcional
120219 Ecuaciones diferenciales ordinarias
Keywords: Fractional boundary value problem
Fixed-point theorem
Positive solution
Issue Date: 2011
Journal: Boundary Value Problems 
Abstract: The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fractional boundary value problem D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ( 1 ) = u ′ ( 0 ) = 0 , where 2 < α ≤ 3 and D 0 + α is the Riemann-Liouville fractional derivative. Our analysis relies on a fixed-point theorem in partially ordered metric spaces. The autonomous case of this problem was studied in the paper [Zhao et al., Abs. Appl. Anal., to appear], but in Zhao et al. (to appear), the question of uniqueness of the solution is not treated. We also present some examples where we compare our results with the ones obtained in Zhao et al. (to appear). 2010 Mathematics Subject Classification: 34B15
ISSN: 1687-2762
DOI: 10.1186/1687-2770-2011-25
Source: Boundary Value Problems 2011 [ISSN 1687-2762], 2011:25
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