### Some properties of sets, fixed point theorems in ordered product spaces and applications to a nonlinear system of fractional differential equations

Jing Ren, Chengbo Zhai

DOI: http://dx.doi.org/10.12775/TMNA.2016.095

#### Abstract

We study a partial order in product spaces and then present some new properties of sets via the partial order. Based on these properties and monotone iterative technique, we establish some new fixed point theorems in product spaces. As an application, we utilize the main fixed point theorem to study a nonlinear system of fractional differential equations. We get the existence-uniqueness of positive solutions for this system, which complements the existing results of positive solutions for this nonlinear problem in the literature.

#### Keywords

Partial order; product space; fixed point theorem; nonlinear system of fractional differential equations

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