A fractionally time-delayed SD-Van der Pol oscillator with a non-perturbative approach

¹ Department of Mathematics, Faculty of Education, Ain Shams University - Roxy, Cairo, Egypt
² Department of Physics, College of Science, Princess Nourah bint Abdulrahman University - P.O. Box 84428, Riyadh 11671, Saudi Arabia

^(a) E-mail: yusryeldib52@hotmail.com, yusryeldib@edu.asu.edu.eg
^(b) E-mail: nasser522000@gmail.com, nasersaleh@edu.asu.edu.eg (corresponding author)
^(c) E-mail: haalyousef@pnu.edu.sa

Received: 22 January 2023
Accepted: 3 May 2023

Abstract

The primary target of the present article is to use a fast and efficient technique to obtain an analytical solution for a Duffing-Van der Pol-SD (D-VDP-SD) oscillator with a time delay. Depending on the smoothness parameter, this kind of vibration behaves in both discontinuous and smooth dynamical systems. This novel technique is presented for transmission from a nonlinear delay fractional oscillator to a linear classical oscillator with ordinary derivatives. The transformation into an equivalent oscillator is described in detail. Based on the comparison, the convergence of the numerical and analytical solutions appears satisfactory, which is an indicator of the accuracy of the solutions produced by the suggested technique.