From a generalised Helmholtz decomposition theorem to fractional Maxwell equations

Manuel D. Ortigueira; Margarita Rivero; Juan J. Trujillo

doi:10.1016/j.cnsns.2014.09.004

From a generalised Helmholtz decomposition theorem to fractional Maxwell equations

Manuel D. Ortigueira, Margarita Rivero, Juan J. Trujillo

Research output: Contribution to journal › Article

22 Citations (Scopus)

Abstract

The main objective of this paper is to propose a new generalisation of the Helmholtz decomposition theorem for both fractional time and space, which leads to four equations generalising the Maxwell equations that emerge as particular case. To get these results the well-known classical vectorial operators, gradient, divergence, curl, and laplacian are generalised to fractional orders using Grünwald-Letnikov approach.

Original language	English
Pages (from-to)	1036-1049
Number of pages	14
Journal	Communications In Nonlinear Science And Numerical Simulation
Volume	22
Issue number	1-3
DOIs	https://doi.org/10.1016/j.cnsns.2014.09.004
Publication status	Published - May 2015

Keywords

Fractional curl
Fractional divergence
Fractional gradient
Fractional laplacian
Grünwald-Letnikov

Access to Document

10.1016/j.cnsns.2014.09.004Licence: CC BY-NC-ND

Link to publication in Scopus

Fingerprint Dive into the research topics of 'From a generalised Helmholtz decomposition theorem to fractional Maxwell equations'. Together they form a unique fingerprint.

Cite this

Ortigueira, M. D., Rivero, M., & Trujillo, J. J. (2015). From a generalised Helmholtz decomposition theorem to fractional Maxwell equations. Communications In Nonlinear Science And Numerical Simulation, 22(1-3), 1036-1049. https://doi.org/10.1016/j.cnsns.2014.09.004

@article{fa5fc403c7c045229e95a7091980b8c9,

title = "From a generalised Helmholtz decomposition theorem to fractional Maxwell equations",

abstract = "The main objective of this paper is to propose a new generalisation of the Helmholtz decomposition theorem for both fractional time and space, which leads to four equations generalising the Maxwell equations that emerge as particular case. To get these results the well-known classical vectorial operators, gradient, divergence, curl, and laplacian are generalised to fractional orders using Gr{\"u}nwald-Letnikov approach.",

keywords = "Fractional curl, Fractional divergence, Fractional gradient, Fractional laplacian, Gr{\"u}nwald-Letnikov",

author = "Ortigueira, {Manuel D.} and Margarita Rivero and Trujillo, {Juan J.}",

note = "Sem PDF. This work was partially funded by National Funds through the Foundation for Science and Technology of Portugal, under the projects PEst-OE/EEI/UI0066/2011 and by FEDER funds and project MTM2010-16499 from the government of Spain.",

year = "2015",

month = "5",

doi = "10.1016/j.cnsns.2014.09.004",

language = "English",

volume = "22",

pages = "1036--1049",

journal = "Communications In Nonlinear Science And Numerical Simulation",

issn = "1007-5704",

publisher = "Elsevier Science B.V., Amsterdam.",

number = "1-3",

}

TY - JOUR

T1 - From a generalised Helmholtz decomposition theorem to fractional Maxwell equations

AU - Ortigueira, Manuel D.

AU - Rivero, Margarita

AU - Trujillo, Juan J.

N1 - Sem PDF. This work was partially funded by National Funds through the Foundation for Science and Technology of Portugal, under the projects PEst-OE/EEI/UI0066/2011 and by FEDER funds and project MTM2010-16499 from the government of Spain.

PY - 2015/5

Y1 - 2015/5

N2 - The main objective of this paper is to propose a new generalisation of the Helmholtz decomposition theorem for both fractional time and space, which leads to four equations generalising the Maxwell equations that emerge as particular case. To get these results the well-known classical vectorial operators, gradient, divergence, curl, and laplacian are generalised to fractional orders using Grünwald-Letnikov approach.

AB - The main objective of this paper is to propose a new generalisation of the Helmholtz decomposition theorem for both fractional time and space, which leads to four equations generalising the Maxwell equations that emerge as particular case. To get these results the well-known classical vectorial operators, gradient, divergence, curl, and laplacian are generalised to fractional orders using Grünwald-Letnikov approach.

KW - Fractional curl

KW - Fractional divergence

KW - Fractional gradient

KW - Fractional laplacian

KW - Grünwald-Letnikov

UR - http://www.scopus.com/inward/record.url?scp=84916876946&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2014.09.004

DO - 10.1016/j.cnsns.2014.09.004

M3 - Article

AN - SCOPUS:84916876946

VL - 22

SP - 1036

EP - 1049

JO - Communications In Nonlinear Science And Numerical Simulation

JF - Communications In Nonlinear Science And Numerical Simulation

SN - 1007-5704

IS - 1-3

ER -