This paper studies partial differential equation model with the new general fractional derivatives involving the kernels of the extended Mittag–Leffler type functions. An initial boundary value problem for the anomalous diffusion of fractional order is analyzed and considered. The fractional derivative with Mittag–Leffler kernel or also called Atangana and Baleanu fractional derivative in time is taken in the Caputo sense. We obtain results on the existence, uniqueness, and regularity of the solution.

中文翻译：

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带有Mittag–Leffler核的分数阶导数的分数阶扩散方程的正则结果

本文使用新的分数阶导数研究偏微分方程模型，其中涉及扩展的Mittag-Leffler类型函数的核。分析并考虑了分数阶反常扩散的初始边值问题。具有Mittag-Leffler核的分数导数，或在时间上也称为Atangana和Baleanu分数导数，在Caputo意义上采用。我们获得解决方案的存在性，唯一性和规则性的结果。