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Fractional Systems: Theoretical Foundations

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Fractional Dynamical Systems: Methods, Algorithms and Applications

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 402))

Abstract

An overview of the fractional order integro-differential, methods and tools of fractional calculus that are commonly used in control and automation are presented. The presented results mainly concern the fractional differential operators Caputo, Riemann–Liouville and Grünwald–Letnikov, as they are some of the most used in the fields mentioned. Moreover, for zero initial value these operators coincides.

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Acknowledgements

The work of P. Ostalczyk was supported by the National Science Centre Poland Grant Number 2016/23/B/ST7/03686. The work of E. Pawluszewicz is supported with University Work No WZ/WM-IIM/1/2019 Faculty of Mechanical Engineering, Bialystok University of Technology.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Institute of Control and Industrial Electronics, Warsaw University of Technology, Warsaw, Poland

    Piotr Ostalczyk

  2. Institute of Robotics and Mechatronics, Bialystok University of Technology, Bialystok, Poland

    Ewa Pawluszewicz

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  1. Piotr Ostalczyk
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  2. Ewa Pawluszewicz
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Correspondence to Ewa Pawluszewicz .

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Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Piotr Kulczycki

  2. Institute of Control and Computation Engineering, University of Zielona Góra, Zielona Góra, Poland

    Józef Korbicz

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

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Ostalczyk, P., Pawluszewicz, E. (2022). Fractional Systems: Theoretical Foundations. In: Kulczycki, P., Korbicz, J., Kacprzyk, J. (eds) Fractional Dynamical Systems: Methods, Algorithms and Applications. Studies in Systems, Decision and Control, vol 402. Springer, Cham. https://doi.org/10.1007/978-3-030-89972-1_2

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