  In this paper, we establish Liouville type theorems for stable solutions on
the whole space $\mathbb R^N$ to the fractional elliptic equation
  $$(-\Delta)^su=f(u)$$ where the nonlinearity is nondecreasing and convex. We
also obtain a classification of stable solutions to the fractional Lane-Emden
system
  $$\begin{cases}
  (-\Delta)^s u = v^p \mbox{ in }\mathbb R^N
  (-\Delta)^s v = u^q \mbox{ in }\mathbb R^N
  \end{cases}$$ with $p>1$ and $ q>1$. In our knowledge, this is the first
classification result for stable solutions of the fractional Lane-Emden system
in literature.
