  We propose a method to numerically compute fractional derivatives (or the
fractional Laplacian) on the whole real line via Riesz fractional integrals.
The compactified real line is divided into a number of intervals, thus
amounting to a multi-domain approach; after transformations in accordance with
the underlying $Z_{q}$ curve ensuring analyticity of the respective integrands,
the integrals over the different domains are computed with a Clenshaw-Curtis
algorithm. As an example, we consider solitary waves for fractional Korteweg-de
Vries equations and compare these to results obtained with a discrete Fourier
transform.
