The Existence of Positive Solution to Three-Point Singular Boundary Value Problem of Fractional Differential Equation
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2009-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2009/314656 |
| Summary: | 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,+∞)),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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| ISSN: | 1085-3375 1687-0409 |