  In this paper, we present a new pseudo-spectral method to solve the initial
value problem associated to a non-local KdV-Burgers equation involving a
Caputo-type fractional derivative. The basic idea is, using an algebraic map,
to transform the whole real line into a bounded interval where we can apply a
Fourier expansion. Special attention is given to the correct computation of the
fractional derivative in this setting.
