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Positive solutions for multipoint boundary value problem of fractional differential equations. (English) Zbl 1223.34008
The author studies the existence of positive solutions for the boundary value problem
$\begin{cases} D^{\alpha}u(t)~+~f(t,u(t))~=~0,~~t\in (0,1) \text{~~and~~} \alpha \in(2,3),\\ u(0)~=~u^{\prime}(0)~=~0, ~~~ u^{\prime}(1)~=~\sum_{i=1}^{m-2}~a_i~u^{\prime}(\xi_i).\end{cases}\tag{*}$
He proves in Theorem 3.4 that the problem (*) has at least one positive solution. In Theorem 3.5 he shows, under some additional conditions, that the problem (*) has at least three positive solutions.

##### MSC:
 34A08 Fractional ordinary differential equations 26A33 Fractional derivatives and integrals 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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