  We classify finite Morse index solutions of the fractional Lane-Emden
equation $(-\Delta)^{s} u=|u|^{p-1} u \ \ \ \mathbb{R}^n $ for $1<s<2$. For the
local case, $s=1$ and $s=2$ this classification was done by Farina in [10] and
Davila, Dupaigne, Wang and Wei in [8], respectively. Moreover, for the nonlocal
case, $0<s<1$, finite Morse index solutions are classified by Davila, Dupaigne
and Wei in [7].
