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Advances in Modelling and Control of Non-integer-Order Systems pp 47–58Cite as

Fractional Linear Equations with Discrete Operators of Positive Order

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Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 320))

Abstract

The Caputo- and Riemann–Liouville–type fractional order difference initial value problems for linear and semilinear equations are discussed. We take under our consideration the possible solution via the classical \(\mathcal{Z}\)-transform method for any positive order. We stress the formulas that used the concept of discrete Mittag–Leffler fractional function.

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Author information

Authors and Affiliations

  1. Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351, Białystok, Poland

    Dorota Mozyrska & Małgorzata Wyrwas

Authors
  1. Dorota Mozyrska
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  2. Małgorzata Wyrwas
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Corresponding author

Correspondence to Dorota Mozyrska .

Editor information

Editors and Affiliations

  1. Department of Electrical, Control and Computer Engineering, Opole University of Technology, Opole, Poland

    Krzysztof J. Latawiec

  2. Department of Electrical, Control and Computer Engineering, Opole University of Technology, Opole, Poland

    Marian Łukaniszyn

  3. Department of Electrical, Control and Computer Engineering, Opole University of Technology, Opole, Poland

    Rafał Stanisławski

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Mozyrska, D., Wyrwas, M. (2015). Fractional Linear Equations with Discrete Operators of Positive Order. In: Latawiec, K., Łukaniszyn, M., Stanisławski, R. (eds) Advances in Modelling and Control of Non-integer-Order Systems. Lecture Notes in Electrical Engineering, vol 320. Springer, Cham. https://doi.org/10.1007/978-3-319-09900-2_5

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  • DOI: https://doi.org/10.1007/978-3-319-09900-2_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09899-9

  • Online ISBN: 978-3-319-09900-2

  • eBook Packages: EngineeringEngineering (R0)

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