In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

中文翻译：

---

磁场存在下非马氏布朗运动的Fokker-Planck方程

在本研究中，我们以简单的方式提出了Fokker-Planck方程，该方程用于具有普通导数（OD），高斯随机力和广义摩擦记忆核的Langevin运动方程。该方程式可以与有或没有来自谐波势的保守力场相关联。我们将这种方法扩展为在磁场存在下的带电布朗粒子。因此，本方法适用于具有OD，高斯色的热噪声和任何种类的线性力场的朗格文运动方程，该线性力场可以是保守的或不是保守的。将这种方法用于与阻尼强度无关的有色高斯噪声也很简单。