Monte Carlo simulations and fractional kinetics considerations for the Higuchi equation

We highlight some physical and mathematical aspects relevant to the derivation and use of the Higuchi equation. More specifically, the application of the Higuchi equation to different geometries is discussed and Monte Carlo simulations to verify the validity of Higuchi law in one and two dimensions, as well as the derivation of the Higuchi equation under alternative boundary conditions making use of fractional calculus, are presented.