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The generalized nonlocal fractal calculus: an efficient tool for fractal circuit analysis.

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Title: The generalized nonlocal fractal calculus: an efficient tool for fractal circuit analysis.
Authors: Banchuin, Rawid1 (AUTHOR) rawid.ban@siam.edu
Source: COMPEL. 2023, Vol. 42 Issue 6, p1744-1770. 27p.
Subjects: Calculus, Fractals, Electric circuits, Kernel functions, Fractal analysis, Degrees of freedom
Abstract: Purpose: The purpose of this paper is to propose a novel nonlocal fractal calculus scheme dedicated to the analysis of fractal electrical circuit, namely, the generalized nonlocal fractal calculus. Design/methodology/approach: For being generalized, an arbitrary kernel function has been adopted. The condition on order has been derived so that it is not related to the γ-dimension of the fractal set. The fractal Laplace transforms of our operators have been derived. Findings: Unlike the traditional power law kernel-based nonlocal fractal calculus operators, ours are generalized, consistent with the local fractal derivative and use higher degree of freedom. As intended, the proposed nonlocal fractal calculus is applicable to any kind of fractal electrical circuit. Thus, it has been found to be a more efficient tool for the fractal electrical circuit analysis than any previous fractal set dedicated calculus scheme. Originality/value: A fractal calculus scheme that is more efficient for the fractal electrical circuit analysis than any previous ones has been proposed in this work. [ABSTRACT FROM AUTHOR]
Copyright of COMPEL is the property of Emerald Publishing Limited and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 173776151
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: The generalized nonlocal fractal calculus: an efficient tool for fractal circuit analysis.
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  Data: <searchLink fieldCode="AR" term="%22Banchuin%2C+Rawid%22">Banchuin, Rawid</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> rawid.ban@siam.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22COMPEL%22">COMPEL</searchLink>. 2023, Vol. 42 Issue 6, p1744-1770. 27p.
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  Data: <searchLink fieldCode="DE" term="%22Calculus%22">Calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Fractals%22">Fractals</searchLink><br /><searchLink fieldCode="DE" term="%22Electric+circuits%22">Electric circuits</searchLink><br /><searchLink fieldCode="DE" term="%22Kernel+functions%22">Kernel functions</searchLink><br /><searchLink fieldCode="DE" term="%22Fractal+analysis%22">Fractal analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Degrees+of+freedom%22">Degrees of freedom</searchLink>
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  Data: Purpose: The purpose of this paper is to propose a novel nonlocal fractal calculus scheme dedicated to the analysis of fractal electrical circuit, namely, the generalized nonlocal fractal calculus. Design/methodology/approach: For being generalized, an arbitrary kernel function has been adopted. The condition on order has been derived so that it is not related to the γ-dimension of the fractal set. The fractal Laplace transforms of our operators have been derived. Findings: Unlike the traditional power law kernel-based nonlocal fractal calculus operators, ours are generalized, consistent with the local fractal derivative and use higher degree of freedom. As intended, the proposed nonlocal fractal calculus is applicable to any kind of fractal electrical circuit. Thus, it has been found to be a more efficient tool for the fractal electrical circuit analysis than any previous fractal set dedicated calculus scheme. Originality/value: A fractal calculus scheme that is more efficient for the fractal electrical circuit analysis than any previous ones has been proposed in this work. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of COMPEL is the property of Emerald Publishing Limited and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1108/COMPEL-03-2023-0113
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      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 27
        StartPage: 1744
    Subjects:
      – SubjectFull: Calculus
        Type: general
      – SubjectFull: Fractals
        Type: general
      – SubjectFull: Electric circuits
        Type: general
      – SubjectFull: Kernel functions
        Type: general
      – SubjectFull: Fractal analysis
        Type: general
      – SubjectFull: Degrees of freedom
        Type: general
    Titles:
      – TitleFull: The generalized nonlocal fractal calculus: an efficient tool for fractal circuit analysis.
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            – D: 01
              M: 11
              Text: 2023
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              Y: 2023
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              Value: 42
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