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The existence of positive solutions of singular fractional boundary value problems. (English) Zbl 1228.34020
Summary: We discuss the existence of positive solutions for the singular fractional boundary value problem $$D^{\alpha }u+f(t,u,u',D^{\mu }u)=0$$, $$u(0)=0$$, $$u'(0)=u'(1)=0$$, where $$2<\alpha <3$$, $$0<\mu <1$$. Here $$D^{\alpha }$$ is the standard Riemann-Liouville fractional derivative of order $$\alpha$$, $$f$$ is a Carathéodory function and $$f(t,x,y,z)$$ is singular at the value $$0$$ of its arguments $$x,y,z$$.

##### MSC:
 34A08 Fractional ordinary differential equations and fractional differential inclusions 34B99 Boundary value problems for ordinary differential equations
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