Time-fractional diffusion equation with time dependent diffusion coefficient

We consider the time-fractional diffusion equation with time dependent diffusion coefficient given by (0O(C)tW)-W-alpha(x,t)=D(alpha,gamma)t(gamma)[partial derivative W-2(x,t)/partial derivative x(2)], where O-0((C)t)alpha is the Caputo operator. We investigate its solutions in the infinite and the finite domains. The mean squared displacement and the mean first passage time are also considered. In particular, for alpha=0, the mean squared displacement is given by < x(2)>similar to t(gamma) and we verify that the mean first passage time is finite for superdiffusive regimes.