This paper starts by introducing the Grünwald-Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy-Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.
|Original language||English (US)|
|Journal||Journal of Statistical Mechanics: Theory and Experiment|
|State||Published - Sep 30 2014|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was partially funded by National Funds through the Foundation for Science and Technology of Portugal, under the project PEst-OE/EEI/UI0066/2011.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty