In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By the adjoint system corresponding to our diffusion equation, we construct useful quantitative relation between unknowns and measurements. From Laplace transform and the knowledge in complex analysis, the uniqueness theorem is proved.

中文翻译：

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从稀疏边界数据唯一确定分数阶扩散方程中的分数阶和源项

在本文中，对于二维分数阶扩散方程，我们研究了从稀疏边界测量值同时恢复分数阶和源项的逆问题。通过对应于我们的扩散方程的伴随系统，我们在未知数和测量值之间构建了有用的定量关系。从拉普拉斯变换和复分析中的知识，证明了唯一性定理。