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Fractional integro-differential calculus and its control-theoretical applications. I. Mathematical fundamentals and the problem of interpretation

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Abstract

The review is devoted to using the fractional integro-differential calculus for description of the dynamics of various systems and control processes. Consideration was given to the basic notions of the fractional integro-differential calculus and the problem of interpretation of the fractional operators. Presented were examples of physical systems described in terms of the apparatus under consideration.

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    A. G. Butkovskii, S. S. Postnov & E. A. Postnova

  2. Moscow State University, Moscow, Russia

    E. A. Postnova

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Original Russian Text © A.G. Butkovskii, S.S. Postnov, E.A. Postnova, 2013, published in Avtomatika i Telemekhanika, 2013, No. 4, pp. 3–42.

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Butkovskii, A.G., Postnov, S.S. & Postnova, E.A. Fractional integro-differential calculus and its control-theoretical applications. I. Mathematical fundamentals and the problem of interpretation. Autom Remote Control 74, 543–574 (2013). https://doi.org/10.1134/S0005117913040012

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