Riesz potential versus fractional Laplacian

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

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

Riesz potential versus fractional Laplacian

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

Research output: Contribution to journal › Article › peer-review

12 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 language	English (US)
Pages (from-to)	P09032
Journal	Journal of Statistical Mechanics: Theory and Experiment
Volume	2014
Issue number	9
DOIs	https://doi.org/10.1088/1742-5468/2014/09/P09032
State	Published - 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

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10.1088/1742-5468/2014/09/P09032

Cite this

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title = "Riesz potential versus fractional Laplacian",

abstract = "This paper starts by introducing the Gr{\"u}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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AU - Ortigueira, Manuel Duarte

AU - Laleg-Kirati, Taous-Meriem

AU - Machado, José António Tenreiro

N1 - 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.

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N2 - 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.

AB - 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.

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SP - P09032

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 9

ER -

Riesz potential versus fractional Laplacian

Abstract

Bibliographical note

ASJC Scopus subject areas

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