A continuous variant for Grünwald-Letnikov fractional derivatives |
| |
Authors: | Marie-Christine Néel Ali Abdennadher |
| |
Institution: | a UMRA Climat Sol Environnement, INRA d’Avignon, Domaine Saint Paul- Site Agroparc, F-84914 Avignon Cedex 9, France b Department of Mathematics, Institut National des Sciences Appliquées et de Technologie, Centre Urbain Nord, BP 676 Cedex 1080 Charguia Tunis, Tunisia c Department of Mathematics and Informatics, University of Antananarivo, Antananarivo, Madagascar |
| |
Abstract: | The names of Grünwald and Letnikov are associated with discrete convolutions of mesh h, multiplied by h−α. When h tends to zero, the result tends to a Marchaud’s derivative (of the order of α) of the function to which the convolution is applied. The weights of such discrete convolutions form well-defined sequences, proportional to k−α−1 near infinity, and all moments of integer order r<α are equal to zero, provided α is not an integer. We present a continuous variant of Grünwald-Letnikov formulas, with integrals instead of series. It involves a convolution kernel which mimics the above-mentioned features of Grünwald-Letnikov weights. A first application consists in computing the flux of particles spreading according to random walks with heavy-tailed jump distributions, possibly involving boundary conditions. |
| |
Keywords: | 05 60 -k 46 65 +g 05 40 Fb 02 60 Nm |
本文献已被 ScienceDirect 等数据库收录! |
|