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Existence and multiplicity of positive solutions for singular fractional boundary value problems. (English) Zbl 1247.34006

Summary: We discuss the existence and multiplicity of positive solutions for the singular fractional boundary value problem

D 0+ α u(t)+f((t,u(t),D 0+ ν u(t),D 0+ μ u(t))=0,
u(0)=u ' (0)=u '' (0)=u '' (1)=0,

where 3<α4, 0<ν1, 1<μ2, D 0+ α is the standard Riemann-Liouville fractional derivative, f is a Carathédory function and f(t,x,y,z) is singular at the value 0 of its arguments x,y,z. By means of a fixed point theorem, the existence and multiplicity of positive solutions are obtained.

MSC:
34A08Fractional differential equations
34B18Positive solutions of nonlinear boundary value problems for ODE
34B16Singular nonlinear boundary value problems for ODE
45J05Integro-ordinary differential equations
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