Before revision: The energy dissipation is an important and essential property of classical phase-field equations . 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.
After revision: The energy dissipation is an important and essential property of classical phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the existence of both nonlocality and nonlinearity.