Abstract Two inverse problems with final overdetermination for diffusion and wave equations containing the Caputo fractional time derivative and a fractional Laplacian of distributed order are considered. They are: 1) the problem to reconstruct a time-dependent source term; 2) the problem to recover simultaneously the source term, the order of the time derivative and the fractional Laplacian. Uniqueness of solutions of these problems is proved. Sufficient conditions for the uniqueness are stricter for the 2nd problem than for the 1st problem.

中文翻译：

---

从最终数据确定非局部扩散和波动方程的时间相关源和参数

摘要 考虑了包含 Caputo 分数阶时间导数和分布阶分数 Laplacian 的扩散和波动方程的最终超定的两个反问题。它们是： 1) 重建与时间相关的源项的问题；2）同时恢复源项、时间导数阶数和分数拉普拉斯算子的问题。证明了这些问题的解的唯一性。唯一性的充分条件对于第二个问题比对于第一个问题更严格。