In this paper, we study some properties of the generalized Fokker–Planck equation induced by the time-changed fractional Ornstein–Uhlenbeck process. First of all, we exploit some sufficient conditions to show that a mild solution of such equation is actually a classical solution. Then, we discuss an isolation result for mild solutions. Finally, we prove the weak maximum principle for strong solutions of the aforementioned equation and then a uniqueness result.

中文翻译：

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时变分数 Ornstein-Uhlenbeck 随机过程的 Fokker-Planck 方程

在本文中，我们研究了由时变分数 Ornstein-Uhlenbeck 过程引起的广义 Fokker-Planck 方程的一些性质。首先，我们利用一些充分条件来证明该方程的温和解实际上是经典解。然后，我们讨论温和解的隔离结果。最后，我们证明了上述方程的强解的弱极大原理，然后证明了唯一性结果。