The Complex Order Fractional Derivatives and Systems are Non Hermitian

Manuel D. Ortigueira

doi:10.1007/978-3-031-04383-3_3

The Complex Order Fractional Derivatives and Systems are Non Hermitian

Manuel D. Ortigueira

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Citations (Scopus)

7 Downloads (Pure)

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 language	English
Title of host publication	Proceedings of the International Conference on Fractional Differentiation and its Applications, ICFDA 2021
Editors	Andrzej Dzielinski, Dominik Sierociuk, Piotr Ostalczyk
Publisher	Springer
Pages	38-44
Number of pages	7
ISBN (Electronic)	978-3-031-04383-3
ISBN (Print)	978-3-031-04382-6
DOIs	https://doi.org/10.1007/978-3-031-04383-3_3
Publication status	Published - 2022
Event	International Conference on Fractional Calculus and its Applications, 2021 - Virtual, Online Duration: 6 Sept 2021 → 8 Sept 2021

Publication series

Name	Lecture Notes in Networks and Systems
Publisher	Springer, Cham
Volume	452 LNNS
ISSN (Print)	2367-3370
ISSN (Electronic)	2367-3389

Conference

Conference	International Conference on Fractional Calculus and its Applications, 2021
City	Virtual, Online
Period	6/09/21 → 8/09/21

Keywords

Complex order
Hermitian derivative
Liouville derivative

Access to Document

10.1007/978-3-031-04383-3_3

cmplxorder icfdaAccepted author manuscript, 318 KB

Cite this

Ortigueira, M. D. (2022). The Complex Order Fractional Derivatives and Systems are Non Hermitian. In A. Dzielinski, D. Sierociuk, & P. Ostalczyk (Eds.), Proceedings of the International Conference on Fractional Differentiation and its Applications, ICFDA 2021 (pp. 38-44). (Lecture Notes in Networks and Systems; Vol. 452 LNNS). Springer. https://doi.org/10.1007/978-3-031-04383-3_3

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Ortigueira, MD 2022, The Complex Order Fractional Derivatives and Systems are Non Hermitian. in A Dzielinski, D Sierociuk & P Ostalczyk (eds), Proceedings of the International Conference on Fractional Differentiation and its Applications, ICFDA 2021. Lecture Notes in Networks and Systems, vol. 452 LNNS, Springer, pp. 38-44, International Conference on Fractional Calculus and its Applications, 2021, Virtual, Online, 6/09/21. https://doi.org/10.1007/978-3-031-04383-3_3

The Complex Order Fractional Derivatives and Systems are Non Hermitian. / Ortigueira, Manuel D.
Proceedings of the International Conference on Fractional Differentiation and its Applications, ICFDA 2021. ed. / Andrzej Dzielinski; Dominik Sierociuk; Piotr Ostalczyk. Springer, 2022. p. 38-44 (Lecture Notes in Networks and Systems; Vol. 452 LNNS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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