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Nonlocal fractal calculus based analyses of electrical circuits on fractal set.

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Title: Nonlocal fractal calculus based analyses of electrical circuits on fractal set.
Authors: Banchuin, Rawid1 (AUTHOR) rawid.ban@siam.edu
Source: COMPEL. 2022, Vol. 41 Issue 1, p528-549. 22p.
Subjects: Fractals, Electric circuits, Calculus, Lagrange equations, Resistor-inductor-capacitor circuits, Fractal analysis, Cantor sets
Abstract: Purpose: The purpose of this paper is to present the analyses of electrical circuits with arbitrary source terms defined on middle b cantor set by means of nonlocal fractal calculus and to evaluate the appropriateness of such unconventional calculus. Design/methodology/approach: The nonlocal fractal integro-differential equations describing RL, RC, LC and RLC circuits with arbitrary source terms defined on middle b cantor set have been formulated and solved by means of fractal Laplace transformation. Numerical simulations based on the derived solutions have been performed where an LC circuit has been studied by means of Lagrangian and Hamiltonian formalisms. The nonlocal fractal calculus-based Lagrangian and Hamiltonian equations have been derived and the local fractal calculus-based ones have been revisited. Findings: The author has found that the LC circuit defined on a middle b cantor set become a physically unsound system due to the unreasonable associated Hamiltonian unless the local fractal calculus has been applied instead. Originality/value: For the first time, the nonlocal fractal calculus-based analyses of electrical circuits with arbitrary source terms have been performed where those circuits with order higher than 1 have also been analyzed. For the first time, the nonlocal fractal calculus-based Lagrangian and Hamiltonian equations have been proposed. The revised contradiction free local fractal calculus-based Lagrangian and Hamiltonian equations have been presented. A comparison of local and nonlocal fractal calculus in terms of Lagrangian and Hamiltonian formalisms have been made where a drawback of the nonlocal one has been pointed out. [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.)
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DbLabel: Engineering Source
An: 154835135
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  Data: Nonlocal fractal calculus based analyses of electrical circuits on fractal set.
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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>. 2022, Vol. 41 Issue 1, p528-549. 22p.
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  Data: <searchLink fieldCode="DE" term="%22Fractals%22">Fractals</searchLink><br /><searchLink fieldCode="DE" term="%22Electric+circuits%22">Electric circuits</searchLink><br /><searchLink fieldCode="DE" term="%22Calculus%22">Calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Lagrange+equations%22">Lagrange equations</searchLink><br /><searchLink fieldCode="DE" term="%22Resistor-inductor-capacitor+circuits%22">Resistor-inductor-capacitor circuits</searchLink><br /><searchLink fieldCode="DE" term="%22Fractal+analysis%22">Fractal analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Cantor+sets%22">Cantor sets</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Purpose: The purpose of this paper is to present the analyses of electrical circuits with arbitrary source terms defined on middle b cantor set by means of nonlocal fractal calculus and to evaluate the appropriateness of such unconventional calculus. Design/methodology/approach: The nonlocal fractal integro-differential equations describing RL, RC, LC and RLC circuits with arbitrary source terms defined on middle b cantor set have been formulated and solved by means of fractal Laplace transformation. Numerical simulations based on the derived solutions have been performed where an LC circuit has been studied by means of Lagrangian and Hamiltonian formalisms. The nonlocal fractal calculus-based Lagrangian and Hamiltonian equations have been derived and the local fractal calculus-based ones have been revisited. Findings: The author has found that the LC circuit defined on a middle b cantor set become a physically unsound system due to the unreasonable associated Hamiltonian unless the local fractal calculus has been applied instead. Originality/value: For the first time, the nonlocal fractal calculus-based analyses of electrical circuits with arbitrary source terms have been performed where those circuits with order higher than 1 have also been analyzed. For the first time, the nonlocal fractal calculus-based Lagrangian and Hamiltonian equations have been proposed. The revised contradiction free local fractal calculus-based Lagrangian and Hamiltonian equations have been presented. A comparison of local and nonlocal fractal calculus in terms of Lagrangian and Hamiltonian formalisms have been made where a drawback of the nonlocal one has been pointed out. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  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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      – Type: doi
        Value: 10.1108/COMPEL-06-2021-0210
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 22
        StartPage: 528
    Subjects:
      – SubjectFull: Fractals
        Type: general
      – SubjectFull: Electric circuits
        Type: general
      – SubjectFull: Calculus
        Type: general
      – SubjectFull: Lagrange equations
        Type: general
      – SubjectFull: Resistor-inductor-capacitor circuits
        Type: general
      – SubjectFull: Fractal analysis
        Type: general
      – SubjectFull: Cantor sets
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      – TitleFull: Nonlocal fractal calculus based analyses of electrical circuits on fractal set.
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              M: 01
              Text: 2022
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