An approach of Banach algebra in fuzzy metric spaces with an application

The purpose of this paper is to present a new concept of a Banach algebra in a fuzzy metric space (FM-space). We define an open ball, an open set and prove that every open ball in an FM-space over a Banach algebra $ \mathcal{A} $ is an open set. We present some more topological properties and a Hausdorff metric on FM-spaces over $ \mathcal{A} $. Moreover, we state and prove a fuzzy Banach contraction theorem on FM-spaces over a Banach algebra $ \mathcal{A} $. Furthermore, we present an application of an integral equation and will prove a result dealing with the integral operators in FM-spaces over a Banach algebra.