Abstract
We consider the homogeneous time-fractional diffusion equation \partial^{\alpha} (u-u_0)(t)+A u(t)=0, \quad t\text{-a.e.} Here, \partial^{\alpha} denotes the Riemann–Liouville fractional derivative of order \alpha \in (0,1) with respect to time and A is a uniformly elliptic operator on \mathbb{R}^d . We prove decay estimates in time and other regularity properties for the solution of the above equation.
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