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Existence and uniqueness of strictly nondecreasing and positive solution for a fractional three-point boundary value problem. (English) Zbl 1235.34024

Summary: We consider the following nonlinear fractional three-point boundary value problem

D 0+ α u(t)+f(t,u(t))=0,0<t<1,3<α4,u(0)=u ' (0)=u '' (0)=0,u '' (1)=βu '' (η),

where D 0+ α is the standard Riemann-Liouville fractional derivative. By using a fixed point theorem in partially ordered sets, we obtain sufficient conditions for the existence and uniqueness of positive and nondecreasing solution to the above boundary value problem.

34A08Fractional differential equations
34B10Nonlocal and multipoint boundary value problems for ODE
34B18Positive solutions of nonlinear boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
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