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Existence and uniqueness of positive solutions for a singular fractional three-point boundary value problem. (English) Zbl 1246.34006
Summary: We investigate the existence and uniqueness of positive solutions for the following singular fractional three-point boundary value problem D 0 + α u(t)+f(t,u(t))=0,0<t<1,u(0)=u ' (0)=u '' (0)=0,u '' (1)=βu '' (η), where 3<α4,D 0 + α is the standard Riemann-Liouville derivative and f:(0,1]×[0,)[0,) with lim t0 + f(t,·)= (i.e., f is singular at t=0). Our analysis relies on a fixed point theorem in partially ordered metric spaces.
34A08Fractional differential equations
47H10Fixed point theorems for nonlinear operators on topological linear spaces
34B10Nonlocal and multipoint boundary value problems for ODE