Separation of variables for the fractional laplacian

Question

Consider the fractional Laplacian of $u\in H^{s}(\mathbb{R}^n)$ denoted as $(-\Delta)^s u$ with $s\in (0,1)$. I know that in general for the usual Laplacian we can write $\Delta = \Delta_r + r^{-2}\Delta_{\mathbb{S}^{n-1}}$ where $\mathbb{S}^{n-1}$ is the $n-1$ dimensional sphere and $r$ is the radial part. Do we have a similar decomposition for the fractional Laplacian as well?