Superderivations and Jordan superderivations of generalized quaternion algebras

Let $H_{\alpha,\beta}$ be the generalized quaternion algebra over a unitary commutative ring. This paper aims to consider superderivations and Jordan superderivations of $H_{\alpha,\beta}$ and hence to obtain the superalgebra $Der_{s} (H_{\alpha,\beta})$ of superderivations and $Der_{Js} (H_{\alpha,\beta})$ of Jordan superderivations of $H_{\alpha,\beta}$. It turns out that on generalized quaternion algebras, any superderivation is inner. In particular, there exist Jordan superderivations that are not superderivations.