Abstract
The goal of this paper is to present a new class of contraction mappings, so-called eta`theta- contractions. Also, in the context of partially ordered metric spaces, some coupled fixed-point results for eta`theta-contraction mappings are introduced. Furthermore, to support our results, two examples are provided. Finally, the theoretical results are applied to obtain the existence of solutions to coupled fractional differential equations with a Mittag-Leffler kernel.