Albert Einstein, in his work regarding Brownian motion (1905) entitled "On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat", gave the definitive confirmation that atoms and molecules exist. Since then, many works have suggested that the classical diffusion equation derived by Einstein does not apply in some more complex systems (where the mean square displacement of a particle is not proportional to time).

In this work, we discuss the validity of fractional calculus in modeling anomalous-diffusion processes, and we derive a robust numerical method to solve the Time-Fractional-Diffusion-Equation that takes into account the singularity introduced by the fractional operator.