TY - JOUR
T1 - Riesz potential versus fractional Laplacian
AU - Ortigueira, Manuel Duarte
AU - Laleg-Kirati, Taous Meriem
AU - Machado, Jose Tenreiro
N1 - 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 - 2014/9/1
Y1 - 2014/9/1
N2 - This paper starts by introducing the Gru ̈nwald–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 Gru ̈nwald–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.
KW - dynamics
KW - nonlinear
KW - nonlinear dynamics
U2 - 10.1088/1742-5468/2014/09/P09032
DO - 10.1088/1742-5468/2014/09/P09032
M3 - Article
VL - stacks.iop.org/JSTAT/2014/P09032
SP - 1
EP - 11
JO - Journal of Statistical Mechanics: Theory and Experiment
JF - Journal of Statistical Mechanics: Theory and Experiment
IS - NA
ER -