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Zbl 1149.26012
El-Shahed, Moustafa
Positive solutions for boundary value problem of nonlinear fractional differential equation. (English)
[J] Abstr. Appl. Anal. 2007, Article ID 10368, 8 p. (2007). ISSN 1085-3375; ISSN 1687-0409/e

Summary: We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem: $D_{0+}^{\alpha}u(t)+\lambda a(t) f(u(t))=0$, $0<t<1$, $u(0)=u'(0)=u'(1)=0$, where $2<\alpha<3$ is a real number and $D_{0+}^\alpha$ is the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results.

MSC 2000:: *26A33 Fractional derivatives and integrals (real functions)
34K10 Boundary value problems for functional-differential equations

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