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Fractional integro-differential calculus and its control-theoretical applications. I: Mathematical fundamentals and the problem of interpretation. (English. Russian original) Zbl 1275.93039

Autom. Remote Control 74, No. 4, 543-574 (2013); translation from Avtom. Telemekh. 2013, No. 4, 3-42 (2013).
Summary: The review is devoted to using the fractional integro-differential calculus for description of the dynamics of various systems and control processes. Consideration is focussed to the basic notions of the fractional integro-differential calculus and the problem of interpretation of the fractional operators. Examples of physical systems are presented described in terms of the apparatus under consideration.

MSC:

93C15 Control/observation systems governed by ordinary differential equations
34A08 Fractional ordinary differential equations
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