Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

Tomasz Stefański; Jacek Gulgowski

doi:10.3390/e23080987

Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

Abstract

In this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their properties from the point of view of classical electrodynamics, i.e., energy and momentum conservation, reciprocity, causality. Afterwards, we derive classical solutions for wave-propagation problems, assuming helical, spherical, and cylindrical symmetries of solutions. The results are supported by numerical simulations and their analysis. Discussion of relations between the TF Schrödinger equation and TF electrodynamics is included as well.

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Authors (2)

Tomasz Stefański dr hab. inż.
Jacek Gulgowski
- Uniwersytet Gdański

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DOI:: Digital Object Identifier (open in new tab) 10.3390/e23080987
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Category:: Articles
Type:: artykuły w czasopismach
Published in:: ENTROPY no. 23,
ISSN: 1099-4300
Language:: English
Publication year:: 2021
Bibliographic description:: Stefański T., Gulgowski J.: Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector// ENTROPY-SWITZ -Vol. 23,iss. 8 (2021), s.987-
DOI:: Digital Object Identifier (open in new tab) 10.3390/e23080987
Verified by:: Gdańsk University of Technology