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Existence, uniqueness, and multiplicity results on positive solutions for a class of Hadamard-type fractional boundary value problem on an infinite interval. (English) Zbl 1452.34017

Summary: This paper focuses on a class of Hadamard-type fractional differential equation with nonlocal boundary conditions on an infinite interval. New existence, uniqueness, and multiplicity results of positive solutions are obtained by using Schauder’s fixed point theorem, Banach’s contraction mapping principle, the monotone iterative method, and the Avery-Peterson fixed point theorem. Examples are included to illustrate our main results.

MSC:

34A08 Fractional ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B40 Boundary value problems on infinite intervals for ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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