Riesz potential versus fractional Laplacian

Manuel Duarte Ortigueira, Taous-Meriem Laleg-Kirati, José António Tenreiro Machado

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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 languageEnglish (US)
Pages (from-to)P09032
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number9
StatePublished - Sep 30 2014

Bibliographical note

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.

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Riesz potential versus fractional Laplacian'. Together they form a unique fingerprint.

Cite this