In this paper, on the basis of the reproducing kernel functions, a novel meshless algorithm is explored for fractional advection–diffusion-reaction equations (ADREs) with Caputo time variable order. Firstly, the Gaussian kernel function and the Mittag–Leffler kernel function are introduced and combined to construct a new binary reproducing kernel function. Secondly, base on the constructed reproducing kernel function, by employing the space–time collocation technique, a novel meshless method is proposed for fractional ADREs. Numerical experiments are implemented and the numerical results show the potential of our new approach for fractional ADREs.

中文翻译：

---

再现基于核函数的无序分数阶对流扩散反应方程

本文在再现核函数的基础上，探索了一种新的无网格算法，用于求解Caputo时变阶数的分数对流-扩散-反应方程（ADRE）。首先，引入并组合了高斯核函数和Mittag-Leffler核函数，以构造一个新的二进制再生核函数。其次，在构造的再生核函数的基础上，采用时空配置技术，提出了一种新型的无网格方法用于分数ADRE。进行了数值实验，数值结果表明了我们的新方法用于分数ADRE的潜力。