This study is devoted to recovering two initial values for a time‐fractional diffusion‐wave equation from boundary Cauchy data. We provide the uniqueness result for recovering two initial values simultaneously by the method of Laplace transformation and analytic continuation. And then we use a nonstationary iterative Tikhonov regularization method to solve the inverse problem and propose a finite dimensional approximation algorithm to find good approximations to the initial values. Numerical examples in one‐ and two‐dimensional cases are provided to show the effectiveness of the proposed method.

中文翻译：

---

时分扩散波方程的两个初始值同时反演

这项研究致力于从边界柯西数据中为时间分数阶扩散波方程恢复两个初始值。我们提供了通过拉普拉斯变换和解析连续法同时恢复两个初始值的唯一性结果。然后，我们使用非平稳迭代Tikhonov正则化方法来解决反问题，并提出了有限维近似算法，以找到与初始值的良好近似。提供一维和二维情况下的数值示例，以证明该方法的有效性。