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On a New Symmetric Fractional Variable Order Derivative

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Theoretical Developments and Applications of Non-Integer Order Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 357))

Abstract

The paper presents particular definitions of symmetric fractional variable order derivatives. The \(\mathcal {AD}\) and \(\mathcal {DA}\) types of the fractional variable order derivatives and their properties have been introduced. Additionally, the switching order schemes equivalent to these types of definitions have been shown. Finally, the theoretical considerations have been validated on numerical examples.

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Acknowledgments

This work was supported by the Polish National Science Center with the decision number DEC-2011/03/D/ST7/00260.

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Authors and Affiliations

  1. Institute of Control and Industrial Electronics, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland

    Dominik Sierociuk, Wiktor Malesza & Michal Macias

Authors
  1. Dominik Sierociuk
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  2. Wiktor Malesza
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  3. Michal Macias
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Corresponding author

Correspondence to Dominik Sierociuk .

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Editors and Affiliations

  1. Faculty of Electrical Engineering, West Pomeranian University of Technology, Szczecin, Poland

    Stefan Domek

  2. Faculty of Electrical Engineering, West Pomeranian University of Technology, Szczecin, Poland

    Paweł Dworak

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Sierociuk, D., Malesza, W., Macias, M. (2016). On a New Symmetric Fractional Variable Order Derivative. In: Domek, S., Dworak, P. (eds) Theoretical Developments and Applications of Non-Integer Order Systems. Lecture Notes in Electrical Engineering, vol 357. Springer, Cham. https://doi.org/10.1007/978-3-319-23039-9_3

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  • DOI: https://doi.org/10.1007/978-3-319-23039-9_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23038-2

  • Online ISBN: 978-3-319-23039-9

  • eBook Packages: EngineeringEngineering (R0)

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