  In this paper, we study the local behavior of nonnegative solutions of
fractional semi-linear equations $(-\Delta)^\sigma u = u^p$ with an isolated
singularity, where $\sg \in (0, 1)$ and $\frac{n}{n-2\sg} < p <
\frac{n+2\sg}{n-2\sg}$. We first use blow up method and a Liouville type
theorem to derive an upper bound. Then we establish a monotonicity formula and
a sufficient condition for removable singularity to give a classification of
the isolated singularities. When $\sg=1$, this classification result has been
proved by Gidas and Spruck (Comm. Pure Appl. Math. 34: 525-598, 1981).
