Riesz potential versus fractional Laplacian

Manuel Duarte Ortigueira, Taous Meriem Laleg-Kirati, Jose Tenreiro Machado

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1-11
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue numberNA
Publication statusPublished - 1 Sep 2014


  • nonlinear dynamics


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