Fixed point results of fuzzy mappings with applications

Jleli and Samet introduced the notion of $\mathcal{F}$-metric space as a generalization of traditional metric space and proved Banach contraction principle in the setting of these generalized metric spaces. The aim of this article is to utilize $\mathcal{F}$-metric space and establish some common $\alpha$-fuzzy fixed point theorems for rational ( $\beta$- $\varphi )$-contractive conditions. Our results extend, generalize and unify some well-known results in the literature. As application of our main result, we discuss the solution of fuzzy integrodifferential equations in the setting of a generalized Hukuhara derivative.