论文标题
时间衍生化的fokker-planck方程的精确解决方案：一种新颖的方法
Exact Solutions of the Time Derivative Fokker-Planck Equation: A Novel Approach
论文作者
论文摘要
在本文中，提出了一种方法来找到分数fokker-planck方程的精确解决方案。它基于通过HOPF变换将其转换为一阶部分微分方程的系统，并实现扩展的统一方法。另一方面，将分数衍生物还原为非自主普通衍生物。因此，分数fokker-planck方程还原为非自主古典方程。获得了一些经典的，分数衍生物fokker-Planck方程的明确解。结果表明，Fokker-Planck方程的解决方案是双陶斯的。发现高摩擦系数在降低标准偏差方面起着重要作用。此外，发现部分比分形具有更强的作用。值得一提的是，高斯的混合物是机器学习中的强大工具。此外，当改变分数时间衍生物的顺序时，会导致概率分布函数的轻微影响。同样，这表明速度的均值和平方平方变化缓慢。
In the present article, an approach to find the exact solution of the fractional Fokker-Planck equation is presented. It is based on transforming it to a system of first-order partial differential equation via Hopf transformation, together with implementing the extended unified method. On the other hand, reduction of the fractional derivatives to non autonomous ordinary derivative. Thus the fractional Fokker-Planck equation is reduced to non autonomous classical ones. Some explicit solutions of the classical, fractional time derivative Fokker-Planck equation, are obtained . It is shown that the solution of the Fokker-Planck equation is bi-Gaussian's. It is found that high friction coefficient plays a significant role in lowering the standard deviation. Further, it is found the fractionality has stronger effect than fractality. It is worthy to mention that the mixture of Gaussian's is a powerful tool in machine learning. Further, when varying the order of the fractional time derivatives, results to slight effects in the probability distribution function. Also, it is shown that the mean and mean square of the velocity vary slowly.
