  We derive monotonicity formulae for solutions of the fractional
H\'{e}non-Lane-Emden equation \begin{equation*} (-\Delta)^{s} u=|x|^a |u|^{p-1}
u \ \ \ \text{in } \ \ \mathbb{R}^n, \end{equation*} when $0<s<2$, $a>0$ and
$p>1$. Then, we apply these formulae to classify stable solutions of the above
equation.
