This paper is devoted to identifying the fractional order and diffusion coefficient in a time fractional diffusion wave equation from boundary observation data in one dimensional case. The uniqueness of recovering the fractional order and diffusion coefficient simultaneously has been proved by the Laplace transform and Gel’fand-Levitan theory. In addition, we apply the iterative regularizing ensemble Kalman method to provide a numerical implementation of the considered inverse problem. Four numerical examples are carried out to demonstrate the performance of the proposed method.

中文翻译：

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确定分数阶扩散波方程中的分数阶和扩散系数

本文致力于从一维情况下的边界观测数据中识别时间分数扩散波方程中的分数阶和扩散系数。Laplace变换和Gel'fand-Levitan理论已经证明了同时恢复分数阶和扩散系数的独特性。另外，我们应用迭代正则化集成卡尔曼方法来提供所考虑的反问题的数值实现。进行了四个数值算例，以证明所提出方法的性能。