A reliable numerical algorithm for fractional Lienard equation arising in oscillating circuits

This work presents a numerical approach for handling a fractional Lienard equation (FLE) arising in an oscillating circuit. The scheme is based on the Vieta Lucas operational matrix of the fractional Liouville-Caputo derivative and the collocation method. This methodology involves a systematic appro...

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 7; pp. 19557 - 19568
Main Authors Singh, Jagdev, Kumar, Jitendra, Kumar, Devendra, Baleanu, Dumitru
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
collocation method
error analysis
fractional lienard equation
operational matrix of differentiation
vieta lucas polynomials
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ISSN2473-6988
2473-6988
DOI10.3934/math.2024954

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Summary:This work presents a numerical approach for handling a fractional Lienard equation (FLE) arising in an oscillating circuit. The scheme is based on the Vieta Lucas operational matrix of the fractional Liouville-Caputo derivative and the collocation method. This methodology involves a systematic approach wherein the operational matrix aids in expressing the fractional problem in terms of non-linear algebraic equations. The proposed numerical approach utilizing the operational matrix method offers a vital solution framework for efficiently tackling the fractional Lienard equation, addressing a key challenge in mathematical modeling. To analyze the fractional order system, we derive an approximate solution for the FLE. The solutions are explained graphically and in tabular form.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024954