Riesz potential versus fractional Laplacian

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

doi:10.1088/1742-5468/2014/09/P09032

Riesz potential versus fractional Laplacian

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

Research output: Contribution to journal › Article

7 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	1-11
Journal	Journal of Statistical Mechanics: Theory and Experiment
Volume	stacks.iop.org/JSTAT/2014/P09032
Issue number	NA
DOIs	https://doi.org/10.1088/1742-5468/2014/09/P09032
Publication status	Published - 1 Sep 2014

Keywords

nonlinear dynamics

Access to Document

10.1088/1742-5468/2014/09/P09032

Cite this

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

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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.

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