Common fixed point results in $ \mathcal{F} $-metric spaces with application to nonlinear neutral differential equation

The aim of this article is to obtain common fixed point results for generalized contractions involving control functions of two variables in the context of $ \mathcal{F} $-metric spaces. We also furnish an example to show the originality of our main result. Some results in the context of $ \mathcal{F} $-metric space equipped with a directed graph $ G $ are also established. As an application, we discuss the existence of solution to nonlinear neutral differential equation.