Abstract and Applied Analysis
Volume 2009 (2009), Article ID 314656, 18 pages
doi:10.1155/2009/314656

The existence of positive solution to three-point singular boundary value problem of fractional differential equation

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(q−1)/2u(t)|t=ξ, where 1<q≤2 is a real number, ξ∈(0,1/2], α∈(0,+∞) and αΓ(q)ξ(q−1)/2<Γ((q+1)/2),Dq is the standard Riemann-Liouville fractional derivative, and f∈C((0,1]×[0,+∞),[0,+∞)),lim⁡t→+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.