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Positive solutions for a class of singular fractional boundary value problems. (English) Zbl 1235.34010

Summary: We investigate the existence and uniqueness of positive solutions for the following singular fractional boundary value problem

D 0 + α u(t)+f(t,u(t))=0,0<t<1,u(0)=u(1)=0,

where 1<α2,D 0 + α is the standard Riemann-Liouville differentiation 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 sets.

MSC:
34A08Fractional differential equations
34B18Positive solutions of nonlinear boundary value problems for ODE
34B16Singular nonlinear boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
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