Numerical Investigation of the Fractional-Order Liénard and Duffing Equations Arising in Oscillating Circuit Theory

Abstract

In this article, we present the Jacobi spectral colocation method to solve the fractional model of Linard and Duffing equations with the Liouville-Caputo fractional derivative. These equations are the generalization of the spring-mass system equation and describe the oscillating circuit. The main reason for using this technique is high accuracy and low computational cost compared to some other methods. The main solution behaviors of these equations are due to fractional orders, which are explained graphically. The convergence analysis of the proposed method is also provided. A comparison is made between the exact and approximate solutions.

Topics & Concepts