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

Jagdev Singh; Jitendra Kumar; Devendra Kumar; Dumitru Baleanu; Jagdev Singh; Jitendra Kumar; Devendra Kumar; Dumitru Baleanu

doi:10.3934/math.2024954

AIMS Mathematics

2024, Volume 9, Issue 7: 19557-19568. doi: 10.3934/math.2024954

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

1.
Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India
2.
Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, 02447, Korea
3.
Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India
4.
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
5.
Institute of Space Sciences-Subsidiary of INFLPR, Magurele-Bucharest, Romania

Received: 31 January 2024 Revised: 10 April 2024 Accepted: 18 April 2024 Published: 13 June 2024
MSC : 26A33, 33C45, 65L05

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.
- fractional Lienard equation,
- operational matrix of differentiation,
- Vieta Lucas polynomials,
- collocation method,
- error analysis
Citation: Jagdev Singh, Jitendra Kumar, Devendra Kumar, Dumitru Baleanu. A reliable numerical algorithm for fractional Lienard equation arising in oscillating circuits[J]. AIMS Mathematics, 2024, 9(7): 19557-19568. doi: 10.3934/math.2024954

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Abstract

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.

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