  In this paper, we propose a novel pseudospectral method to approximate
accurately and efficiently the fractional Laplacian without using truncation.
More precisely, given a bounded regular function defined over $\mathbb R$, we
map the unbounded domain into a finite one, then we represent the function as a
trigonometrical series. Therefore, the central point of this paper is the
computation of the fractional Laplacian of an elementary trigonometric
function.
  As an application of the method, we also do the simulation of Fisher's
equation with fractional Laplacian in the monostable case.
