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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 α u+f(t,u,u ' ,D μ u)=0, u(0)=0, u ' (0)=u ' (1)=0, where 2<α<3, 0<μ<1. Here D α is the standard Riemann-Liouville fractional derivative of order α, f is a Carathéodory function and f(t,x,y,z) is singular at the value 0 of its arguments x,y,z.
34A08Fractional differential equations
34B99Boundary value problems for ODE
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