  In this paper, we first establish decay estimates for the fractional and
higher-order fractional H\'enon-Lane-Emden systems by using a nonlocal average
and integral estimates, which deduce a result of non-existence. Next, we apply
the method of scaling spheres introduced in \cite{DQ2} to derive a Liouville
type theorem. We also construct an interesting example on super
$\frac{\alpha}{2}$-harmonic functions (Proposition 1.2).
