Propagation of waves in fractal spaces

Abstract

In this study, we study waves propagation in fractal spaces based on two independent variational approaches: the first one is based on the ‘product-like fractal measure’ introduced by Li and Ostoja-Starzewski in their analysis of nonlinear fractal dynamics in anisotropic porous media whereas the second and another is based on fractal calculus, which includes analytical functions with fractal support. The first approach is motivating since it describes physics in anisotropic media characterized by fractal dimensions. The second one is also of particular importance since it offers a new framework to reformulate the laws of physics in spaces with fractional dimensions. In both approaches, the fractional Laplace equation is derived and solved using plausible boundary conditions. This study proves the importance of fractals in wave motion We show that these models are able to describe the propagation of waves in a fractal Hausdorff dimensional space.