Fixed Point Results for α , ⊥ F -Contractions in Orthogonal F -Metric Spaces with Applications

Abstract

The main objective of this article is to introduce the notion of $\left(\alpha ,{\perp }_{\mathcal{F}}\right)$ -contraction in the setting of orthogonal $\mathcal{F}$ -metric space and present some new fixed point results in such newly introduced space. We also furnish an example to manifest the originality of the obtained results. As application of our foremost result, we look into the solution of a nonlinear fractional differential equation.