The physical interpretation of a variable-order fractional diffusion equation within the framework of the multiple trapping model is presented. This interpretation enables the development of a numerical Monte Carlo algorithm to solve the associated subdiffusion equation. An important feature of the model is variation in energy density of localized states, when the detailed balance condition between localized and mobile particles is satisfied. The variable order anomalous diffusion equations under consideration can be applied to the description of transient subdiffusion in inhomogeneous materials, the order of which depends on the considered spatial and/or time scale. Examples of numerical solutions for different situations are demonstrated. Considering variable-order fractional drift, we calculate and analyze the transient current curves of the time-of-flight method for samples with varying density of localized states.

中文翻译：

---

变阶分数扩散：多重捕获模型中的物理解释和模拟


提出了多重捕获模型框架内的变阶分数扩散方程的物理解释。这种解释使得能够开发数值蒙特卡罗算法来求解相关的子扩散方程。该模型的一个重要特征是当满足局域粒子和移动粒子之间的详细平衡条件时，局域态能量密度的变化。所考虑的变阶反常扩散方程可应用于描述非均匀材料中的瞬态次扩散，其阶数取决于所考虑的空间和/或时间尺度。演示了不同情况下数值解的示例。考虑变阶分数漂移，我们计算并分析了不同局域态密度样品的飞行时间法瞬态电流曲线。