“…Fractional derivatives are used in physics to model anomalous diffusion, where a cloud of particles spreads farther and faster than the classical diffusion model predicts (Barkai et al, 2000;Blumen et al, 1989;Bouchaud and Georges, 1990;Klafter et al, 1987;Meerschaert et al, 1999Meerschaert et al, , 2002aMeerschaert et al, , 2002bKlafter, 2000, 2004;Saichev and Zaslavsky, 1997;Zaslavsky, 1994). Fractional derivative models have also been proposed in finance (Gorenflo et al, 2001;Raberto et al, 2002;Sabatelli et al, 2002;Scalas et al, 2000Scalas et al, , 2005Scalas, 2006) to model price volatility, and in hydrology , Benson et al, 2000a, 2000bSchumer et al, 2001Schumer et al, , 2003 to model fast spreading of pollutants. In each case, the fractional derivative term substitutes for the classical second derivative term, resulting in a wider and faster spread.…”