Random front propagation in fractional diffusive systems

Modelling the propagation of interfaces is of interest in several fields of applied sciences, such as those involving chemical reactions where the reacting interface separates two different compounds. When the front propagation occurs in systems characterized by an underlying random motion, the front gets a random character and a tracking method for fronts with a random motion is desired. The Level Set Method, which is a successful front tracking technique widely used for interfaces with deterministic motion, is here randomized assuming that the motion of the interface is characterized by a random diffusive process. In particular, here we consider the case of a motion governed by the time-fractional diffusion equation, leading to a probability density function for the interface particle displacement given by the M-Wright/Mainardi function. Some numerical results are shown and discussed.