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2009 The Existence of Positive Solution to Three-Point Singular Boundary Value Problem of Fractional Differential Equation
Yuansheng Tian, Anping Chen
Abstr. Appl. Anal. 2009: 1-18 (2009). DOI: 10.1155/2009/314656

Abstract

We investigate the existence of positive solution to nonlinear fractional differential equation three-point singular boundary value problem: Dqu(t)+f(t,u(t))=0, 0<t<1, u(0)=0, u(1)=αD(q1)/2u(t)|t=ξ, where 1<q2 is a real number, ξ(0,1/2], α(0,+) and αΓ(q)ξ(q1)/2<Γ((q+1)/2),Dq is the standard Riemann-Liouville fractional derivative, and fC((0,1]×[0,+),[0,+)),limt+0f(t,)=+ (i.e., f is singular at t=0). By using the fixed-point index theory, the existence result of positive solutions is obtained.

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Yuansheng Tian. Anping Chen. "The Existence of Positive Solution to Three-Point Singular Boundary Value Problem of Fractional Differential Equation." Abstr. Appl. Anal. 2009 1 - 18, 2009. https://doi.org/10.1155/2009/314656

Information

Published: 2009
First available in Project Euclid: 16 March 2010

zbMATH: 1190.34004
MathSciNet: MR2521129
Digital Object Identifier: 10.1155/2009/314656

Rights: Copyright © 2009 Hindawi

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