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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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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