In this study, to overcome the limitations of non-singular fractional derivatives in the Caputo–Fabrizio and Atangana–Baleanu senses (especially in dealing with the variable-order (VO) fractional calculus), we introduce a new non-singular VO fractional derivative with Mittag–Leffler function as its kernel. Some useful results are derived from this fractional derivative. Moreover, this fractional derivative is used for introducing the VO fractional version of the 2D Richard equation. A meshless scheme based on the thin plate spline radial basis functions (RBFs) is developed for solving this equation. The validity of the formulated method is investigated through three numerical examples.

中文翻译：

---

具有非奇异 Mittag-Leffler 核的新变阶分数阶导数：应用于二维理查德方程的变阶分数阶数

在这项研究中，为了克服 Caputo-Fabrizio 和 Atangana-Baleanu 意义中非奇异分数阶导数的局限性（特别是在处理可变阶 (VO) 分数阶微积分时），我们引入了一种新的非奇异分数阶导数以 Mittag-Leffler 函数为核。一些有用的结果来自这个分数导数。此外，该分数阶导数用于引入二维 Richard 方程的 VO 分数形式。开发了一种基于薄板样条径向基函数 (RBF) 的无网格方案来求解该方程。通过三个数值例子研究了公式化方法的有效性。