Abstract
Is there a relation between fractional calculus and fractal geometry? Can a fractional order system be represented by a causal dynamical model? These are the questions recently debated in the scientific community. The author intends to answer these questions. In the first part of the paper, some recently suggested models are reviewed and no convincing evidence is found for any dynamic model of a fractional order system having been built with the help of fractals. Linear filters with lumped constant parameters have a very limited use as approximations of fractional order systems. The model suggested in the paper is a state-space representation with parameters as functions of the independent variable. Regularization of fractional differentiation is considered and asymptotic error estimates, as well as simulation results, are presented.
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Republished from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 3, pp. 393–404, December, 1995.
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Rutman, R.S. On physical interpretations of fractional integration and differentiation. Theor Math Phys 105, 1509–1519 (1995). https://doi.org/10.1007/BF02070871
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DOI: https://doi.org/10.1007/BF02070871