Numerical Solution of Fractional Electrical Circuits by Haar Wavelet

Ahmed, Sahar Altaf; Khan, Sumaira Yousuf

doi:10.11113/matematika.v35.n3.1205

Cited by 3 publications

(3 citation statements)

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“…The generalization of electrical signal propagation and more accurate modeling of circuit components are made possible by the use of fractional differential terms in electrical circuits [40][41][42]. The Laplace transform method [43,44], Sumudu transform method [45], Legendre Wavelet Method using Riemann-Liouville fractional derivative definition [46], and Haar wavelet method using Caputo fractional derivative definition [47] are the numerical solution methods for fractional circuit equations developed up to now. The equations created by using the Caputo fractional derivative expression are subjected to a numerical Laplace transform by Gomez et al [43], and their solutions in the time domain are derived in terms of the Mittag-Leffler function.…”

Section: Introductionmentioning

confidence: 99%

“…In another study, Gill et al [45] obtain the solutions of fractional RLC circuits in terms of Mittag-Leffler function using Sumudu transform. Arora and Chauan [46] use the Legendre wavelet method for the solution of these fractional circuit equations, while Altaf and Khan [47] examine the Haar wavelet method for similar fractional RLC circuit solutions.…”

Section: Introductionmentioning

confidence: 99%

“…In this study, approximate solutions of fractional order LC, RC and RLC circuit equations given in equations (1)-( 3) [47] with two wavelet methods are discussed.…”

Section: Introductionmentioning

confidence: 99%

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Wavelet methods for fractional electrical circuit equations

Tural-Polat,

Dincel

2023

Phys. Scr.

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Classical electric circuits consists of resistors, inductors and capacitors which have irreversible and lossy properties that are not taken into account in classical analysis. FDEs can be interpreted as basic memory operators and are generally used to model the lossy properties or defects. Therefore, employing fractional differential terms in electric circuit equations provides accurate modelling of those circuit elements. In this paper, the numerical solutions of fractional LC, RC and RLC circuit equations are considered to better model those imperfections. To this end, the operational matrices for Bernoulli and Chebyshev wavelets are used to obtain the numerical solutions of those fractional circuit equations. Chebyshev wavelets are orthogonal, and under some circumstances, Bernoulli wavelets can be orthogonal. The wavelet methods' quick convergence and minimal processing load depend on the orthogonality principle. In the proposed method, those FDEs are transformed into algebraic equation systems using operational matrices employing the discrete Wavelets. The performance of those two wavelet methods are compared and contrasted for computational load, speed, and absolute error values. The paper exploits discrete Bernoulli and Chebyshev wavelets for the numerical solution of fractional LC, RC and RLC circuit equations. The fast convergence, low processing burden, and compactness of the Bernoulli and Chebyshev wavelet methods for fractional circuit equation solutions represent the novel contributions of this paper. Numerical solutions and comparisons are also presented to validate the method.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Wavelet methods for fractional electrical circuit equations

Tural-Polat,

Dincel

2023

Phys. Scr.

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Application of fractional modified taylor wavelets in the dynamical analysis of fractional electrical circuits under generalized caputo fractional derivative

Rayal,

Anand,

Srivastava

2024

Phys. Scr.

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This study examines the application of fractional calculus in the analysis and modeling of electrical circuits of fractional order, highlighting its potential to explain the behaviour of complex electrical circuits accurately. In the domain of electrical circuits, fractional differential equations are employed in the analysis and simulation of systems that consist of resistors, capacitors and inductors. In the present paper, a novel approach utilizing fractional order modified Taylor wavelets is implemented to solve the fractional model of RL, LC, RC and RLC electrical circuits under generalized Caputo fractional derivative which offers precise and flexible modeling of non-locality and hereditary characteristics in complex systems. Furthermore, an additional parameter $\sigma$ (time scale parameter) is incorporated in fractional circuit dynamics to maintain the physical dimensionality. The considered wavelets with the collocation technique offer an efficient solution by converting the fractional model of electrical circuits into a set of algebraic equations which are further solved by using the Newton iteration method. Moreover, this study discusses the significance of Ulam-Hyers stability, emphasizing its role in ensuring stable and reliable circuit performance. The impact of fractional order on the dynamics of the electric circuit model is presented by tables and graphs. The approximate solutions obtained by the proposed method are well comparable with exact solutions and some other existing wavelet-based techniques. The residual errors are also evaluated under various model parameters for fractional orders. Furthermore, the graphs illustrate that the error progressively decreases as the number of wavelets basis increases.

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