Time-fractional Allen-Cahn and Cahn-Hilliard phase-field models and their numerical investigation

For time fractional Cahn-Hilliard model, we observe from the numerical results that the bigger the fractional order α is, the faster the energy decays. However, for time fractional Allen-Cahn model, we derived an opposite conclusion. Moreover, we also study the coarsening dynamics for time fractional Cahn-Hilliard model, numerical results reveal that the scaling law for the energy decays as O(t−α3), which is consistent with the well-known result O(t−13) for integer order Cahn-Hilliard model.