## 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 $D^{\alpha}_{0+}u(t)+f(t,u(t))=0,~0<t<1,~1<\alpha\leq 2,$ 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:

 34A08 Fractional ordinary differential equations 26A33 Fractional derivatives and integrals 45J05 Integro-ordinary differential equations
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### References:

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