Abstract This paper is devoted to determine the fractional order, the initial flux speed and the boundary Neumann data simultaneously in a one-dimensional time-fractional diffusion-wave equation from part boundary Cauchy observation data. We prove the uniqueness result for this inverse problem by using a new result for the Mittag-Leffler function and Laplace transform combining with analytic continuation. Then we use the iterative regularizing ensemble Kalman method in Bayesian framework to solve the inverse problem numerically. And four numerical examples are provided to show the effectiveness and stability of the proposed algorithm.

中文翻译：

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部分边界柯西数据同时识别时间分数阶扩散波方程中的三个参数

摘要 本文致力于从部分边界柯西观测数据中同时确定一维时间分数扩散波方程中的分数阶数、初始通量速度和边界诺依曼数据。我们通过使用 Mittag-Leffler 函数和拉普拉斯变换结合解析延拓的新结果证明了该逆问题的唯一性结果。然后我们使用贝叶斯框架中的迭代正则化集成卡尔曼方法来数值求解逆问题。并提供了四个数值例子来说明所提算法的有效性和稳定性。