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Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations. (English) Zbl 1189.34014

Summary: We are concerned with the nonlinear differential equation of fractional order

${D}_{0+}^{\alpha }u\left(t\right)+f\left(t,u\left(t\right)\right)=0,\phantom{\rule{3.33333pt}{0ex}}0

where ${D}_{0+}^{\alpha }$ is the standard Riemann-Liouville fractional derivative, subject to the boundary conditions $u\left(0\right)=0$, ${D}_{0+}^{\beta }u\left(1\right)=a{D}_{0+}^{\beta }u\left(\xi \right)$. We obtain the existence and multiplicity results of positive solutions by using some fixed point theorems.

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