TITLE

The Existence of Positive Solution to Three-Point Singular Boundary Value Problem of Fractional Differential Equation

AUTHOR(S)
Yuansheng Tian; Anping Chen
PUB. DATE
January 2009
SOURCE
Abstract & Applied Analysis;2009, Special section p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
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= , 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, +∞)), 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.
ACCESSION #
55252794

 

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