From a generalised Helmholtz decomposition theorem to fractional Maxwell equations

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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)1036-1049
Number of pages14
JournalCommunications In Nonlinear Science And Numerical Simulation
Volume22
Issue number1-3
DOIs
Publication statusPublished - May 2015

Keywords

  • Fractional curl
  • Fractional divergence
  • Fractional gradient
  • Fractional laplacian
  • Grünwald-Letnikov

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