Fractional Diffusion Equation for Fractal-Time-Continuous-Time Random Walks

It is pointed out that the spherical symmetric diffusion equation of fractional order for the time, recently proposed by E.Roman and Giona [J.Phys.A2 5(1992)2107-21171: dt l’d”P(r,t) = -A corresponds, for integer spatial dimensions d = 1 and d = 3, to the long time description of a the fractal-time continuous-time random- walk, in which the interjump density has the asymptotic form Q(t) -t-i--?, with 0 < 7 = 2/d, < 1.