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On the recursive fractional variable-order derivative: equivalent switching strategy, duality, and analog modeling. (English) Zbl 1342.94132

Summary: In this paper, a switching strategy for recursive fractional variable-order derivative is proposed. This strategy can be interpreted as an explanation of order switching mechanism for this particular type of derivative. Additionally, important properties of variable fractional order derivatives, required for prove the main result, are introduced both in a difference equation and a matrix form. Duality between the recursive and standard variable-order derivative is detailed derived. Based on the switching scheme, an analog realization of the recursive variable-order derivative definition is presented. Experimental results obtained for the analog realization are compared to the numerical results.

MSC:

94C05 Analytic circuit theory
26A33 Fractional derivatives and integrals
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