  In this paper, we characterize the local superderivations on Cartan type Lie
superalgebras over the complex field $\mathbb{C}$. Furthermore, we prove that
every local superderivations on Cartan type simple Lie superalgebras is a
superderivations. As an application, using the results on local
superderivations we characterize the $2$-local superderivations on Cartan type
Lie superalgebras. We prove that every $2$-local superderivations on Cartan
type Lie superalgebras is a superderivations.

Rings and Algebras