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.A 25(1992)2107–2117]: 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 ψ(t) t−1−γ, with 0 < γ = 2/dw < 1.