Carlson iterating rational approximation and performance analysis of fractional operator with arbitrary order

Qiu-Yan He(何秋燕)^{1}, Bo Yu(余波)^{2}, Xiao Yuan(袁晓)^{1}

1 College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China; 2 College of Physics and Engineering, Chengdu Normal University, Chengdu 611130, China

Abstract The performance analysis of the generalized Carlson iterating process, which can realize the rational approximation of fractional operator with arbitrary order, is presented in this paper. The reasons why the generalized Carlson iterating function possesses more excellent properties such as self-similarity and exponential symmetry are also explained. K-index, P-index, O-index, and complexity index are introduced to contribute to performance analysis. Considering nine different operational orders and choosing an appropriate rational initial impedance for a certain operational order, these rational approximation impedance functions calculated by the iterating function meet computational rationality, positive reality, and operational validity. Then they are capable of having the operational performance of fractional operators and being physical realization. The approximation performance of the impedance function to the ideal fractional operator and the circuit network complexity are also exhibited.

Qiu-Yan He(何秋燕), Bo Yu(余波), Xiao Yuan(袁晓) Carlson iterating rational approximation and performance analysis of fractional operator with arbitrary order 2017 Chin. Phys. B 26 040202

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