2-local derivations on Witt algebras

In this paper, we prove that every 2-local derivation on Witt algebras $W_n, W_n^+$ or $W_n^{++}$ is a derivation for all $n=1,2,\cdots,\infty$. As a consequence we obtain that every 2-local derivation on any centerless generalized Virasoro algebra of higher rank is a derivation.