Asymptotic Properties of Solutions of the Fractional Diffusion-Wave   Equation
  For the fractional diffusion-wave equation with the Caputo-Dzhrbashyan fractional derivative of order $\alpha \in (1,2)$ with respect to the time variable, we prove an analog of the principle of limiting amplitude (well-known for the wave equation and some other hyperbolic equations) and a pointwise stabilization property of solutions (similar to a well-known property of the heat equation and some other parabolic equations). 
Anatoly N. Kochubei
math.AP math-ph math.MP