The aim of this paper is to introduce the notions of $\alpha$-$(\mathcal F,H)$-$(\varphi,\psi)$ and $\mu$-$(\mathcal F,H)$-$(\varphi,\psi)$ contractions and present several coupled fixed point theorems for this type of contractions in the set of ordered metric spaces. Several examples are offered to illustrate the validity of the obtained results. As an application, the existence of a solution of Fredholm nonlinear integral equations are also investigated.