TY - GEN

T1 - Finite difference approximation for the fractional half-curl operator

AU - Kastner, Raphael

N1 - Publisher Copyright:
© 2019 IEEE.

PY - 2019/9

Y1 - 2019/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85074904743&partnerID=8YFLogxK

U2 - 10.1109/ICEAA.2019.8879271

DO - 10.1109/ICEAA.2019.8879271

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AN - SCOPUS:85074904743

T3 - Proceedings of the 2019 21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019

SP - 885

BT - Proceedings of the 2019 21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019

Y2 - 9 September 2019 through 13 September 2019

ER -