Affiliation:
1. Institut de Mathématiques de Bourgogne Université de Bourgogne Dijon Cedex France
2. Institut Universitaire de France Université de Bourgogne Dijon Cedex France
Abstract
AbstractWe 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 multidomain approach; after transformations in accordance with the underlying 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.
Funder
Agence Nationale de la Recherche