In this paper, we consider an inverse problem for time-fractional advection-dispersion equation in a multi-layer composite medium. The main goal of our paper is to approximate the initial information, which is inaccessible for measurement, from the observation data at a certain point in second layer by constructing a regularized solution using a filter regularization method. Under appropriate regularity assumptions of the exact solution, we give convergence rate of the error between the reconstructed solution and the exact one. A numerical example is provided to illustrate the main results.

中文翻译：

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恢复多层多孔介质中的水浓度

在本文中，我们考虑了多层复合介质中时间分数平流色散方程的反问题。我们论文的主要目标是通过使用滤波器正则化方法构建正则化解，从第二层某个点的观测数据中近似测量无法获得的初始信息。在精确解的适当正则性假设下，我们给出了重构解与精确解之间误差的收敛率。提供了一个数值例子来说明主要结果。