Abstract This paper deals with an inverse problem of the determination of the fractional order in time-fractional diffusion equations from one interior point observation. We give a representation of the solution via the Mittag-Leffler function and eigenfunction expansion, from which the Lipschitz stability of the fractional order with respect to the measured data at the interior point is established.

中文翻译：

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时间分数扩散方程中阶次确定的稳定性结果

摘要 本文研究了从一个内点观测确定时间分数扩散方程分数阶的反问题。我们通过 Mittag-Leffler 函数和特征函数展开给出解的表示，由此建立分数阶相对于内点测量数据的 Lipschitz 稳定性。