The Complex Order Fractional Derivatives and Systems are Non Hermitian

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Abstract

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

Original languageEnglish
Title of host publicationProceedings of the International Conference on Fractional Differentiation and its Applications, ICFDA 2021
EditorsAndrzej Dzielinski, Dominik Sierociuk, Piotr Ostalczyk
PublisherSpringer
Pages38-44
Number of pages7
ISBN (Electronic)978-3-031-04383-3
ISBN (Print) 978-3-031-04382-6
DOIs
Publication statusPublished - 2022
EventInternational Conference on Fractional Calculus and its Applications, 2021 - Virtual, Online
Duration: 6 Sept 20218 Sept 2021

Publication series

NameLecture Notes in Networks and Systems
PublisherSpringer, Cham
Volume452 LNNS
ISSN (Print)2367-3370
ISSN (Electronic)2367-3389

Conference

ConferenceInternational Conference on Fractional Calculus and its Applications, 2021
CityVirtual, Online
Period6/09/218/09/21

Keywords

  • Complex order
  • Hermitian derivative
  • Liouville derivative

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