On Graphical Fuzzy Metric Spaces with Application to Fractional Differential Equations

Abstract

In this article, the authors introduced the concept of graphical fuzzy metric spaces which is a generalization of fuzzy metric spaces with the help of a relation. The authors discussed some topological structure, convergence criteria, and proved a Banach fixed-point result in graphical fuzzy metric space. As an application of obtained results, the authors find a solution of an integral equation and nonlinear fractional differential equations in the context of graphical fuzzy metric spaces. The authors provided some examples to illustrate the obtained results herein.