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 inChinese physics B Vol. 26; no. 4; pp. 66 - 74
Main Author 何秋燕 余波 袁晓
Format Journal Article
LanguageEnglish
Published Chinese Physical Society and IOP Publishing Ltd 01.04.2017
Subjects
approximation error
fractional calculus
fractional operator
generalized Carlson iterating process
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ISSN1674-1056
2058-3834
DOI10.1088/1674-1056/26/4/040202

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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.
AbstractList 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.
Author 何秋燕 余波 袁晓
AuthorAffiliation College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China College of Physics and Engineering, Chengdu Normal University, Chengdu 611130, China
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CitedBy_id crossref_primary_10_3390_fractalfract6070388
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crossref_primary_10_1080_00207217_2020_1727030
crossref_primary_10_1142_S0218126620500838
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Notes 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）
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Snippet The performance analysis of the generalized Carlson iterating process,which can realize the rational approximation of fractional operator with arbitrary...
The performance analysis of the generalized Carlson iterating process, which can realize the rational approximation of fractional operator with arbitrary...
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SubjectTerms approximation error
fractional calculus
fractional operator
generalized Carlson iterating process
Title Carlson iterating rational approximation and performance analysis of fractional operator with arbitrary order
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