标题： 反问题对于具有未知历史的广义分数阶扩散方程 显示英文标题

标题： Inverse problems for a generalized fractional diffusion equation with unknown history

摘要： 反问题对于包含广义分数阶导数的扩散方程进行了研究。 该方程在时间区间$(0,T)$内成立，并假设状态$u$（扩散方程的解）和源$f$在$t\in (t_0,T)$已知，其中$t_0$是$(0,T)$中的某个数。 在$f$满足某些限制条件下，证明了导数的核与椭圆算子的乘积以及$f$对$t\in (0,t_0)$的历史记录都可以唯一恢复。在对$f$限制较少的情况下，展示了核和$f$的历史记录的唯一性。 此外，在当 $u$ 对 $t\in (t_0,T)$的泛函给出时，在未知 $f$的历史情况下证明了核的唯一性。 显示英文摘要

摘要： Inverse problems for a diffusion equation containing a generalized fractional derivative are studied. The equation holds in a time interval $(0,T)$ and it is assumed that a state $u$ (solution of diffusion equation) and a source $f$ are known for $t\in (t_0,T)$ where $t_0$ is some number in $(0,T)$. Provided that $f$ satisfies certain restrictions, it is proved that product of a kernel of the derivative with an elliptic operator as well as the history of $f$ for $t\in (0,t_0)$ are uniquely recovered. In case of less restrictions on $f$ the uniqueness of the kernel and the history of $f$ is shown. Moreover, in a case when a functional of $u$ for $t\in (t_0,T)$ is given the uniqueness of the kernel is proved under unknown history of $f$.