Comparative Analyses of Electrical Circuits with Conventional and Revisited Definitions of Circuit Elements: A Fractional Conformable Calculus Approach

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Research Article: Comparative Analyses of Electrical Circuits with Conventional and Revisited Definitions of Circuit Elements: A Fractional Conformable Calculus Approach
Author: Rawid Banchuin
Email: rawid.ban@siam.edu
Department/Faculty Graduate Schools of IT, Siam University, Bangkok 10160
Published: COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Volume 41, Issue 1, pp. 258-282.

Citation 

Banchuin, R. (2022). Comparative analyses of electrical circuits with conventional and revisited definitions of circuit elements: A fractional conformable calculus approach. COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 41(1), 258-282. https://doi.org/10.1108/COMPEL-03-2021-0079


ABSTRACT

Purpose
The purpose of this paper is to comparatively analyze the electrical circuits defined with the conventional and revisited time domain circuit element definitions in the context of fractional conformable calculus and to promote the combined usage of conventional definitions, fractional conformable derivative and conformable Laplace transform.

Design/methodology/approach
The RL, RC, LC and RLC circuits described by both conventional and revisited time domain circuit element definitions has been analyzed by means of the fractional conformable derivative based differential equations and conformable Laplace transform. The comparison among the obtained results and those based on the methodologies adopted in the previous works has been made.

Findings
The author has found that the conventional definitions-based solution gives a physically reasonable result unlike its revisited definitions-based counterpart and the solutions based on those previous methodologies. A strong agreement to the time domain state space concept-based solution can be observed. The author has also shown that the scalar valued solution can be directly obtained by singularity free conformable Laplace transform-based methodology unlike such state space concept based one.

Originality/value
For the first time, the revisited time domain definitions of resistance and inductance have been proposed and applied together with the revisited definition of capacitance in electrical circuit analyses. The advantage of the combined usage of conventional time definitions, fractional conformable derivative and conformable Laplace transform has been suggested and the impropriety of applying the revisited definitions in circuit analysis has been pointed out.

Keywords: Conformable Laplace transform, Conventional time domain circuit element definition, Fractional conformable derivative, Hamiltonian, Lagrangian, Local fractional derivative, Nonlocal fractional derivative, Revisited time domain circuit element definition, Circuit analysis, Transient analysis, Time domain modelling.


Comparative Analyses of Electrical Circuits with Conventional and Revisited Definitions of Circuit Elements: A Fractional Conformable Calculus Approach

Graduate Schools, Siam University, Bangkok, Thailand

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