An efficient approach to converting the damping fractal models to the traditional system

The general form of the damping fractal Duffing oscillator is considered in this investiga-tion. In this work, the rank of the damping term is not restricted to half the rank of the inertia force. The classical solution of such fractal models cannot be available except for special cases. Due to the complicated fractal problem, a new approach is developed to make the solution available in each case. The approach depends on the idea of converting the fractal models to the equivalent ones in the traditional space. Numerical calculations showed that there is an agreement with the numerical solution when the fractal of the two scales becomes identical to the continuous space. The calculations showed that the decrease in the rank of the inertia force yields a damping behavior, while the decrease in the rank of the damping force leads to suppression of the damping influence of the inertia force. Further, some stability diagrams are plotted to study the stability behavior.(c) 2022 Elsevier B.V. All rights reserved.