标题： 时间分数阶热方程中确定时变主系数的反问题 显示英文标题

标题： Inverse problem of determining time-dependent leading coefficient in the time-fractional heat equation

摘要： 在本文中，我们研究了具有时间依赖主系数的时滞分数阶热方程的直接问题和逆问题。 首先，我们考虑直接问题，并建立了广义解的唯一存在性。 我们还推导了一些正则性结果。 在这里，我们的证明基于特征函数展开方法。 其次，我们研究了确定主系数的逆问题，并证明了该逆问题的适定性。 显示英文摘要

摘要： In this paper, we investigate direct and inverse problems for the time-fractional heat equation with a time-dependent leading coefficient for positive operators. First, we consider the direct problem, and the unique existence of the generalized solution is established. We also deduce some regularity results. Here, our proofs are based on the eigenfunction expansion method. Second, we study the inverse problem of determining the leading coefficient, and the well-posedness of this inverse problem is proved.