TY - JOUR
T1 - Riesz potential versus fractional Laplacian
AU - Ortigueira, Manuel Duarte
AU - Laleg-Kirati, Taous-Meriem
AU - Machado, José António Tenreiro
N1 - KAUST 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.
PY - 2014/9/30
Y1 - 2014/9/30
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/563748
UR - https://iopscience.iop.org/article/10.1088/1742-5468/2014/09/P09032
UR - http://www.scopus.com/inward/record.url?scp=84907495286&partnerID=8YFLogxK
U2 - 10.1088/1742-5468/2014/09/P09032
DO - 10.1088/1742-5468/2014/09/P09032
M3 - Article
SN - 1742-5468
VL - 2014
SP - P09032
JO - Journal of Statistical Mechanics: Theory and Experiment
JF - Journal of Statistical Mechanics: Theory and Experiment
IS - 9
ER -