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

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.

Keywords

• fractional lienard equation
• operational matrix of differentiation
• vieta lucas polynomials
• collocation method
• error analysis