We consider a class of time-fractional phase field models including the Allen-Cahn and Cahn-Hilliard equations. We establish several weighted positivity results for functionals driven by the Caputo time-fractional derivative. Several novel criterions are examined for showing the positive-definiteness of the associated kernel functions. We deduce strict energy-dissipation for a number of non-local energy functionals, thereby proving fractional energy dissipation laws.

翻译：我们考虑的是一组不折不扣的时间阶段场模型,包括艾伦-卡恩和卡恩-希利亚德方程式。我们为卡普托时间折射衍生物驱动的功能设定了几种加权相对性结果。我们研究了几个新的标准,以显示相关内核函数的正确定性。我们推算出一些非本地能源功能的严格能源消耗,从而证明了分数能量消散法。