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The Particular Types of Fractional Variable-Order Symmetric Operators

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Advances in Non-Integer Order Calculus and Its Applications (RRNR 2018)

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Abstract

The paper presents particular definitions of symmetric fractional variable order derivatives. The \(\mathcal {BE}\) and \(\mathcal {EB}\) 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. At the end, all theoretical considerations were validated on numerical examples.

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Acknowledgment

This work was supported by the Polish National Science Center under Grant No. UMO-2014/15/B/ST7/00480.

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Authors and Affiliations

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

    Michal Macias

Authors
  1. Michal Macias
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Correspondence to Michal Macias .

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Editors and Affiliations

  1. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Agnieszka B. Malinowska

  2. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Dorota Mozyrska

  3. Faculty of Electrical Engineering, Bialystok University of Technology, Białystok, Poland

    Łukasz Sajewski

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Macias, M. (2020). The Particular Types of Fractional Variable-Order Symmetric Operators. In: Malinowska, A., Mozyrska, D., Sajewski, Ł. (eds) Advances in Non-Integer Order Calculus and Its Applications. RRNR 2018. Lecture Notes in Electrical Engineering, vol 559. Springer, Cham. https://doi.org/10.1007/978-3-030-17344-9_3

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