Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 22, Issue 1-3, Pages 1036-1049Publisher
ELSEVIER
DOI: 10.1016/j.cnsns.2014.09.004
Keywords
Grunwald-Letnikov; Fractional gradient; Fractional divergence; Fractional curl; Fractional laplacian
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Funding
- National Funds through the Foundation for Science and Technology of Portugal [PEst-OE/EEI/UI0066/2011]
- FEDER
- government of Spain [MTM2010-16499]
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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 Grunwald-Letnikov approach. (C) 2014 Elsevier B.V. All rights reserved.
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