On fixed point results in $ \mathcal{F} $-metric spaces with applications

Abstract

<abstract><p>The aim of this research article is to define locally rational contractions concerning control functions of one variable in the background of $ \mathcal{F} $-metric spaces and establish common fixed point results. We also introduce ($ \alpha ^{\ast } $-$ \psi) $-contractions and generalized ($ \alpha ^{\ast } $, $ \psi, \delta _{\mathcal{F}}) $-contractions in $ \mathcal{F} $-metric spaces and obtain fixed points of multifunctions. A non trivial example is also furnished to manifest the originality of the fundamental result. As application, we investigate the solution of nonlinear neutral differential equation.</p></abstract>