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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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