Abstract In this paper, we have investigated the Langevin and Brownian equations on fractal time sets using F α -calculus and shown that the mean square displacement is not varied linearly with time. We have also generalized the classical method of deriving the Fokker–Planck equation in order to obtain the Fokker–Planck equation on fractal time sets.

中文翻译：

---

康托集上的布朗运动

摘要 在本文中，我们使用 F α -演算研究了分形时间集上的朗之万方程和布朗方程，并表明均方位移不随时间线性变化。我们还推广了推导 Fokker-Planck 方程的经典方法，以获得分形时间集上的 Fokker-Planck 方程。