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首页> 外文期刊>Journal of King Saud University >Analytical approach to Fokker–Planck equation with space- and time-fractional derivatives by means of the homotopy perturbation method
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Analytical approach to Fokker–Planck equation with space- and time-fractional derivatives by means of the homotopy perturbation method

机译：时空导数的Fokker-Planck方程的同伦摄动分析方法

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In this study, we present numerical solutions for the space- and time-fractional Fokker–Planck equation using the homotopy perturbation method (HPM). The fractional derivatives are described in the Caputo sense. The methods give an analytic solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. Some examples are given and comparisons are made, the comparisons show that the homotopy perturbation method is very effective and convenient and overcome the difficulty of traditional methods. The numerical results show that the approaches are easy to implement and accurate when applied to space- and time-fractional Fokker–Planck equations. The methods introduce a promising tool for solving many space–time fractional partial differential equations.
机译：在这项研究中，我们使用同伦扰动方法（HPM）提出了时空分数Fokker-Planck方程的数值解。小数导数以Caputo的含义描述。这些方法以收敛序列的形式给出了具有易于计算的组件的解析解决方案，不需要线性化或小扰动。给出了一些例子并进行了比较，比较表明同态摄动法非常有效，方便，克服了传统方法的困难。数值结果表明，将这些方法应用于空间和时间分数Fokker-Planck方程时，易于实现且准确。这些方法为解决许多时空分数阶偏微分方程提供了一种有前途的工具。

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