Tian Yuansheng

Publications (1)0 Total impact

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

  Tian Yuansheng, Chen Anping
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  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.
  Abstract and Applied Analysis. 01/2009;