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)t^αW(x,t)=D_α,γt^γ[∂²W(x,t)∕∂x²], where ₀O(C)t^α 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 α=0, the mean squared displacement is given by ⟨x²⟩~t^γ and we verify that the mean first passage time is finite for superdiffusive regimes.