Fractional advection–dispersion equations (FADEs) have been widely used in hydrological research to simulate the anomalous solute transport in surface and subsurface water. However, a large gap still exists between real‐world application (i.e., being a prediction tool) and theoretical FADEs. To better understand this disparity, the FADEs are firstly reviewed from the perspective of fractional‐in‐time and fractional‐in‐space, as well as the anomalous characteristics described by those functions. Then, challenges for the application of FADEs are summarized, including the theoretical gap of FADEs that needs multidisciplinary efforts to fill, extensive requirements for computation techniques and mathematical knowledge to apply the FADEs, the poor predictability for most parameters in the FADEs, and the limitations for collecting geologic information of flow fields. Then, some suggestions are given for future work, such as developing excellent code sets and mature simulation software with a friendly interface. This kind of work would alleviate the computation workload of hydrologists, especially those without coding expertise. Summarizing and determining the value ranges of the important parameters are needed (e.g., the order of the fractional derivative), through the extensive field, laboratory, and numerical experiments rather than blindly using their mathematical ranges. It is also needed to perform global sensitivity analysis for the FADEs. Meanwhile, comprehensive comparison work is necessary for suggesting a model suitable for a specific problem. Last but not least, further research is clearly needed to establish a link between nonlocal parameters and the heterogeneity property to develop more efficient fractional order partial differential equations.

中文翻译：

---

分数对流-弥散方程在地表水和地下水中反常溶质运移的应用综述

分数对流扩散方程（FADEs）已被广泛用于水文研究，以模拟溶质在地表和地下水中的异常运移。但是，实际应用（即，作为一种预测工具）与理论上的FADE之间仍然存在很大差距。为了更好地理解这种差异，首先从时间分数和空间分数以及这些函数描述的异常特征的角度对FADE进行了回顾。然后，总结了FADE的应用挑战，包括需要进行多学科努力才能填补的FADE的理论空白，对应用FADE的计算技术和数学知识的广泛要求，FADE中大多数参数的可预测性差，以及收集流场地质信息的局限性。然后，为将来的工作提供了一些建议，例如开发出色的代码集和具有友好界面的成熟仿真软件。这种工作将减轻水文学家的计算工作量，尤其是那些没有编码专业知识的人。需要通过广泛的领域，实验室和数值实验来总结和确定重要参数的值范围（例如，分数阶的阶数），而不是盲目地使用它们的数学范围。还需要对FADE进行全局敏感性分析。同时，需要进行全面的比较工作以提出适合特定问题的模型。最后但并非最不重要的，