Numerical approaches for the computation of fractional derivatives on the whole real line (also called the fractional Laplacian) are discussed. Spectral approaches for the Riesz fractional integrals or Fourier transforms are compared. As an example solitary waves for fractional Korteweg-de Vries and modified Korteweg-de Vries and stationary solutions to the fractional nonlinear Schrödinger equation are constructed.