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    Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter

    Access Status
    Fulltext not available
    Authors
    Zhang, X.
    Wang, L.
    Sun, Qian
    Date
    2014
    Type
    Journal Article
    
    Metadata
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    Citation
    Zhang, X. and Wang, L. and Sun, Q. 2014. Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter. Applied Mathematics and Computations. 226: pp. 708-718.
    Source Title
    Applied Mathematics and Computations
    DOI
    10.1016/j.amc.2013.10.089
    ISSN
    0096-3003
    URI
    http://hdl.handle.net/20.500.11937/31431
    Collection
    • Curtin Research Publications
    Abstract

    In this paper, we study the existence of positive solutions for the following nonlinear fractional differential equations with integral boundary conditions: D0α+u(t) +h(t)f(t,u(t)) = 0, 0<t<1, u(0) = u′(0) = u″(0) = 0, u(1) = λ∫0ηu(s)ds, where 3 < α ≤ 4,0 < η ≤ 1, 0 -< ληαα <1, D0+α is the standard Riemann–Liouville derivative. h(t) is allowed to be singular at t=0 and t=1. By using the properties of the Green function, u0-bounded function and the fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator, we obtain some existence results of positive solution.

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