  In this paper, we give a classification of the isolated singularities of
positive solutions to the semilinear fractional elliptic equations $$(E)
\quad\quad (-\Delta)^s u = |x|^{\theta} u^{p}\quad {\rm in}\ \
B_1\setminus\{0\},\quad u= h\quad{\rm in}\ \ \mathbb{R}^N\setminus B_1,\quad $$
where $s\in(0,1)$, $\theta>-2s$, $p>\frac{N+\theta}{N-2s}$, $B_1$ is the unit
ball centered at the origin of $\mathbb{R}^N$ with $N>2s$. $h$ is a nonnegative
H\"older continuous function in $\mathbb{R}^N\setminus B_1$. Our analysis of
isolated singularities of $(E)$ is based on an integral upper bounds and the
study of the Poisson problem with the fractional Hardy operators. It is worth
noting that our classification of isolated singularity holds in the Sobolev
super critical case $p>\frac{N+2s+2\theta}{N-2s}$ for $s\in(0,1]$ under
suitable assumption of $h$.
