  Herschend-Liu-Nakaoka introduced the notion of $n$-exangulated categories as
higher dimensional analogues of extriangulated categories defined by
Nakaoka-Palu. The class of $n$-exangulated categories contains $n$-exact
categories and $(n+2)$-angulated categories as examples. In this article, we
introduce a notion of Frobenius $n$-exangulated categories which are a
generalization of Frobenius $n$-exact categories. We show that the stable
category of a Frobenius $n$-exangulated category is an $(n+2)$-angulated
category. As an application, this result generalizes the work by Jasso. We
provide a class of $n$-exangulated categories which are neither $n$-exact
categories nor $(n+2)$-angulated categories. Finally, we discuss an application
of the main results and give some examples illustrating it.
