We deal with a class of nonlocal Fokker–Planck equations subject to nonlinear force fields and perturbations, where the questions of global solvability and regularity of solutions will be addressed. A representation of solutions to the Cauchy problem is first derived. Then by using the embeddings of fractional Sobolev spaces and fixed point arguments, we show the existence and Hölder regularity of solutions.

中文翻译：

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具有非线性力场和扰动的非局部 Fokker–Planck 方程

摘要

我们处理一类受非线性力场和扰动影响的非局部福克-普朗克方程，其中将解决全局可解性和解的规律性问题。首先导出柯西问题的解的表示。然后，通过使用分数 Sobolev 空间的嵌入和不动点参数，我们证明了解的存在性和 Hölder 正则性。