Let $(\sigma, \delta)$ be a skew derivation on a ring$R$ Let $q$ be a central $(\sigma, \delta)$ constant. Suppose further that $\delta\sigma = q \cdot \sigma\delta$ Then we say that $(\sigma, \delta)$ is a $q$skew derivation.
16S36 (Associative rings and algebras :: Rings and algebras arising under various constructions :: Ordinary and skew polynomial rings and semigroup rings)