Riesz potential versus fractional Laplacian

Handle URI:
http://hdl.handle.net/10754/563748
Title:
Riesz potential versus fractional Laplacian
Authors:
Ortigueira, Manuel Duarte; Laleg-Kirati, Taous-Meriem ( 0000-0001-5944-0121 ) ; Machado, José António Tenreiro
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Publisher:
IOP Publishing
Journal:
Journal of Statistical Mechanics: Theory and Experiment
Issue Date:
1-Sep-2014
DOI:
10.1088/1742-5468/2014/09/P09032
Type:
Article
ISSN:
17425468
Sponsors:
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.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorOrtigueira, Manuel Duarteen
dc.contributor.authorLaleg-Kirati, Taous-Meriemen
dc.contributor.authorMachado, José António Tenreiroen
dc.date.accessioned2015-08-03T12:08:47Zen
dc.date.available2015-08-03T12:08:47Zen
dc.date.issued2014-09-01en
dc.identifier.issn17425468en
dc.identifier.doi10.1088/1742-5468/2014/09/P09032en
dc.identifier.urihttp://hdl.handle.net/10754/563748en
dc.description.abstractThis 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.en
dc.description.sponsorshipThis work was partially funded by National Funds through the Foundation for Science and Technology of Portugal, under the project PEst-OE/EEI/UI0066/2011.en
dc.publisherIOP Publishingen
dc.subjectnonlinear dynamicsen
dc.titleRiesz potential versus fractional Laplacianen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalJournal of Statistical Mechanics: Theory and Experimenten
dc.contributor.institutionUNINOVA, Faculdade de Ciências e Tecnologia, UNL Campus Da FCT Da UNL, Quinta da TorreCaparica, Portugalen
dc.contributor.institutionINESC-ID, New University of LisbonLisbon, Portugalen
dc.contributor.institutionInstitute of Engineering, Polytechnic of Porto, Dept. of Electrical EngineeringPorto, Portugalen
kaust.authorLaleg-Kirati, Taous-Meriemen
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