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Application of Modified Lucas Wavelets Fractional Approximation Scheme for Analyzing the Fractional Electrical Circuit’s Models

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Abstract

This paper proposes an approximation scheme for electrical circuit models based on the Riemann–Liouville fractional-order derivative. We have considered the derivative’s order as \(0\le \epsilon \le 1\). In this scheme, we initially compute the fractional-order modified Lucas wavelet integrative operational matrix. Subsequently, we employ this approximation technique to transform the equations of fractional-order electrical circuits into a well-established algebraic system, leveraging the fractional-order modified Lucas wavelet integrative operational matrix. This scheme is applied to various fractional electrical circuits including RC, LC, RL and RLC, get good approximate solution. To evaluate the performance of the proposed scheme, we conduct a comparative analysis with existing fractional approximation schemes employing Legendre and Bernoulli wavelets. Our results demonstrate that the proposed scheme performs better than Legendre and Bernoulli wavelets fractional approximation scheme.

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The data used to support the findings of this study are included within the article. There is no additional data and material was used to support this study.

Code Availability

In all experimental application, we used Mathematica 7.0 to perform the calculations, and the CPU running time approximately 10 to 12 s, where used processor is Intel Core i3, 5th generation.

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Acknowledgements

The authors are very grateful to the reviewer for carefully reading the manuscript and for giving such valuable suggestions and comments which have improved the quality and presentation of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, School of Applied and Life Sciences, Uttaranchal University, Dehradun, Uttarakhand, 248007, India

    Madhulika

  2. Department of Mathematics, School of Allied Sciences, Mandsaur University, Mandsaur, Madhyapradesh, 458001, India

    Ankit Kumar

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  1. Madhulika
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Madhulika, Kumar, A. Application of Modified Lucas Wavelets Fractional Approximation Scheme for Analyzing the Fractional Electrical Circuit’s Models. Int. J. Appl. Comput. Math 10, 127 (2024). https://doi.org/10.1007/s40819-024-01728-2

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