Before revision:  Inspired by them, we study in this article the energy dissipation of some numerical schemes for time-fractional phase-field models , including the convex-splitting scheme, the stabilization scheme, and the scalar auxiliary variable scheme. Based on a lemma about a special Cholesky decomposition, it can be proved that the discrete fractional derivative of energy is nonpositive, i.e., the discrete time-fractional energy dissipation law , and that a discrete weighted energy can be constructed to be dissipative, i. e., the discrete weighted energy dissipation law.
After revision:  Inspired by them, we study in this article the energy dissipation of some numerical schemes for time-fractional phase-field models is still incomplete. In this article, we study certain nonlocal-in-time energies using the first-order stabilized semi-implicit L1 scheme. In particular, we will establish a discrete fractional energy law and a discrete weighted energy can be constructed to be dissipative, i. e., the discrete weighted energy dissipation law.