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Zbl 1223.34008
Zhong, Wenyong
(Zhong, Wen-yong)
Positive solutions for multipoint boundary value problem of fractional differential equations. (English)
[J] Abstr. Appl. Anal. 2010, Article ID 601492, 15 p. (2010). ISSN 1085-3375; ISSN 1687-0409/e

The author studies the existence of positive solutions for the boundary value problem $$\cases D^{\alpha}u(t)~+~f(t,u(t))~=~0,~~t\in (0,1) \text{~~and~~} \alpha \in(2,3),\\ u(0)~=~u^{\prime}(0)~=~0, ~~~ u^{\prime}(1)~=~\sum_{i=1}^{m-2}~a_i~u^{\prime}(\xi_i).\endcases\tag*$$ 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.
[Ahmed M. A. El-Sayed (Alexandria)]

MSC 2000:: *34A08
26A33 Fractional derivatives and integrals (real functions)
34B10 Multipoint boundary value problems
34B18 Positive solutions of nonlinear boundary value problems

Keywords: fractional-order differential equations; positive solution; boundary-value problem

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