ANALYTICAL SOLUTION OF THE FRACTAL CUBIC–QUINTIC DUFFING EQUATION

Abstract

In this work, the fractal cubic–quintic Duffing’s equation analytical solution is obtained using the two-scale transform and elliptic functions. Then, the analytical solution is used to study wave propagation in a fractal medium. Since the value of the fractal parameter adjusts the pulse frequency and wavelength propagation velocity, depending upon the fractal medium physical properties, it is found that the information contained in the pulse can be carried out faster over long distances without distortion or loss of intensities. This paper offers a new light on the applicability of the two-scale transform of fractal theory to comprehend natural phenomena.