This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique continuation property. For the numerical reconstruction, the inverse problem is reformulated as an optimization problem with the Tikhonov regularization. We use the Levenberg-Marquardt method to identity the unknown source from noisy measurements. Finally, we give some numerical examples to illustrate the efficiency and accuracy of the proposed algorithm.

翻译：本文研究时空分数阶扩散方程基于后验内部测量的反源问题。利用分数阶导数的记忆效应与唯一延拓性质，建立了该反问题的唯一性结果。在数值重构方面，将反问题重构为带有Tikhonov正则化的优化问题。我们采用Levenberg-Marquardt方法从含噪测量数据中识别未知源项。最后，通过若干数值算例验证了所提算法的有效性与准确性。