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

Authors:
A. G. Butkovskii;S. S. Postnov;E. A. Postnova
Affiliations:
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia;Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia;Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia and Moscow State University, Moscow, Russia
Venue:
Automation and Remote Control
Year:
2013

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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.