Riesz potential versus fractional Laplacian

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

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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
Volume2014
Issue number9
DOIs
StatePublished - Sep 30 2014

ASJC Scopus subject areas

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

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