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

23 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

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

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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.",

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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.",

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AU - Trujillo, Juan J.

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KW - Fractional divergence

KW - Fractional gradient

KW - Fractional laplacian

KW - Grünwald-Letnikov

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