Finite difference approximation for the fractional half-curl operator

Raphael Kastner*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Fractional derivatives [e.g., 1] are almost as old as calculus itself, dating back all the way to Leibniz's times. They find applications in many branches of science, including electromagnetics [2], [3]. Many existing integral definitions seem to have issues with singular functions such as the step function and with distributions [1]. An alternative definition for the half-derivative using derivatives only would be to solve the operator equation mathcal{D} {frac{1}{2}}mathcal{D} {frac{1}{2}}=mathcal{D}, where mathcal{D} is the first derivative operator. This is done most readily in the spectral domain, where trivially mathcal{D} {x} {frac{1}{2}}=sqrt{-jk {x}}. Of particular interest is the half-curl operator [3], [4], whose spectral equivalent is.

Original languageEnglish
Title of host publicationProceedings of the 2019 21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages885
Number of pages1
ISBN (Electronic)9781728105635
DOIs
StatePublished - Sep 2019
Event21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019 - Granada, Spain
Duration: 9 Sep 201913 Sep 2019

Publication series

NameProceedings of the 2019 21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019

Conference

Conference21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019
Country/TerritorySpain
CityGranada
Period9/09/1913/09/19

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