Before revision:  However, it is still unknown if the phase-field models with Caputo time-fractional derivative preserve this property, which is challenging due to the existence of both nonlocality and nonlinearity. Our recent work shows that on the continuous level, the time-fractional energy dissipation law and the weighted energy dissipation law can be achieved.
After revision:  However, it is still unknown if the phase-field models with Caputo time-fractional derivative preserve this property, which is challenging due to the solution such as energy dissipation and maximum principle. Although the theory of energy dissipation for classical phase field models is well established, the weighted energy dissipation law can be achieved.