Carlson iterating rational approximation and performance analysis of fractional operator with arbitrary order
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-simila...
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| Published in | Chinese physics B Vol. 26; no. 4; pp. 66 - 74 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Chinese Physical Society and IOP Publishing Ltd
01.04.2017
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1674-1056 2058-3834 |
| DOI | 10.1088/1674-1056/26/4/040202 |
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| Summary: | 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. |
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| Bibliography: | fractional calculus; fractional operator; generalized Carlson iterating process; approximation error 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 He1, Bo Yu2, and Xiao Yuan1（1 College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China 2College of Physics and Engineering, Chengdu Normal University, Chengdu 611130, China） 11-5639/O4 |
| ISSN: | 1674-1056 2058-3834 |
| DOI: | 10.1088/1674-1056/26/4/040202 |