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Zbl 1189.34014
Li, C.F.; Luo, X.N.; Zhou, Yong
Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations. (English)
[J] Comput. Math. Appl. 59, No. 3, 1363-1375 (2010). ISSN 0898-1221

Summary: We are concerned with the nonlinear differential equation of fractional order $$D^{\alpha}_{0+}u(t)+f(t,u(t))=0,~0<t<1,~1<\alpha\le 2,$$ where $D^{\alpha}_{0+}$ is the standard Riemann-Liouville fractional derivative, subject to the boundary conditions $u(0)=0$, $D^{\beta}_{0+}u(1)=aD^{\beta}_{0+}u(\xi)$. We obtain the existence and multiplicity results of positive solutions by using some fixed point theorems.

MSC 2000:: *34A08
26A33 Fractional derivatives and integrals (real functions)
45J05 Integro-ordinary differential equations

Keywords: Riemann-Liouville derivative; Carathéodory conditions; fractional differential equation; boundary value problem; positive solution

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