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Existence of positive solutions for a kind of nonlinear fractional differential equation with nonlinear boundary value conditions. (English) Zbl 1449.34078

Summary: In this paper, we use mixed monotone operator method to deal with the existence and uniqueness of positive solutions to a class of boundary value problems of the nonlinear fractional order differential equation. Our analysis is based on a new fixed point theorem for mixed monotone operators. As an application, we also give a simple example to illustrate our main conclusions.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34A08 Fractional ordinary differential equations
34B45 Boundary value problems on graphs and networks for ordinary differential equations
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