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Multidimensional Discrete-Time Fractional Calculus of Variations

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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

In this paper a discrete-time multidimensional fractional calculus of variations is introduced. The fractional operators are defined in the sense of Gr\(\ddot{u}\)nvald–Letnikov. We derive necessary optimality conditions and then give examples illustrating the use of obtained results.

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Acknowledgments

Research supported by Bialystok University of Technology grant S/WI/02 /2011 (A. B. Malinowska) and by the Warsaw School of Economics grant KAE/S14/35/15:4 (T. Odzijewicz).

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Authors and Affiliations

  1. Faculty of Computer Science, Bialystok University of Technology, 15-351, Bialystok, Poland

    Agnieszka B. Malinowska

  2. Department of Mathematics and Mathematical Economics, Warsaw School of Economics, 02-554, Warsaw, Poland

    Tatiana Odzijewicz

Authors
  1. Agnieszka B. Malinowska
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  2. Tatiana Odzijewicz
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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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Malinowska, A.B., Odzijewicz, T. (2016). Multidimensional Discrete-Time Fractional Calculus of Variations. 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_2

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  • DOI: https://doi.org/10.1007/978-3-319-23039-9_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23038-2

  • Online ISBN: 978-3-319-23039-9

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