  In this paper, we prove Liouville type theorems for stable solutions to the
weighted fractional Lane-Emden system \begin{align*}
  (-\Delta)^s u = h(x)v^p,\quad (-\Delta)^s v= h(x)u^q, \quad u,v>0\quad
\mbox{in }\;\mathbb{R}^N, \end{align*} where $1<q\leq p$ and $h$ is a positive
continuous function in $\mathbb{R}^N$ satisfying $\displaystyle{\liminf_{|x|\to
\infty}}\frac{h(x)}{|x|^\ell} > 0$ with $\ell > 0.$ Our results generalize the
results established in \cite{HHM16} for the Laplacian case (correspond to
$s=1$) and improve the previous work \cite{TuanHoang21}. As a consequence, we
prove classification result for stable solutions to the weighted fractional
Lane-Emden equation $(-\Delta)^s u = h(x)u^p$ in $\mathbb{R}^N$.
