TECHNICALREPORTS:METHODS Space-time duality for the fractional advection-dispersion equation
TECHNICALREPORTS:METHODS Space-time duality for the fractional advection-dispersion equation
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分数阶对流-弥散方程用空间变量的分数阶导数代替了通常的平流-弥散方程中的二阶空间导数。fi首先应用于地下含水层的示踪剂测试，后来又应用于河流的示踪剂测试。另一种模型将fi第一时间导数替换为时间的分数导数。以前的工作表明，这两个模型都提供了一个合理的fit来突破河流中的曲线，这导致了关于物理上合适的分数模型的争论。本文证明了相关的空间-分数模型与相应的时间-分数模型在数学上是等价的，从而解决了争论。
The fractional advection-dispersion equation replaces the second spatial derivative in the usual advection-dispersion equation with a fractional derivative in the spatial variable. It was first applied to tracer tests in underground aquifers, and later to tracer tests in rivers. An alternative model replaces the first time derivative with a fractional derivative in time. Previous work has shown that both models provide a reason-able fit to breakthrough curves in rivers, which has led to a controversy regarding the physically appropriate fractional model. This paper shows that the relevant space-fractional model is mathematically equivalent to the corresponding time-fractional model, thus resolving the controversy.