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.
|Journal||Journal of Statistical Mechanics: Theory and Experiment|
|Publication status||Published - 1 Sep 2014|
- nonlinear dynamics
Ortigueira, M. D., Laleg-Kirati, T. M., & Machado, J. T. (2014). Riesz potential versus fractional Laplacian. Journal of Statistical Mechanics: Theory and Experiment, stacks.iop.org/JSTAT/2014/P09032(NA), 1-11. https://doi.org/10.1088/1742-5468/2014/09/P09032