Two inverse problems for time-fractional diffusion equation having a family of nonlocal boundary conditions are discussed. In first inverse problem, initial distribution is determined provided that the data at final temperature $t=T$ is given. Second inverse problem addresses the recovery of temporal component of source term whenever total energy of the system is known. A bi-orthogonal system of functions is used to write the series solution by Fourier's method. The classical nature of the solution of both inverse problems is established by using the estimates of Mittag-Leffler function and by imposing some regularity conditions on given datum.

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具有非局部Samarskii-Ionkin型条件的时间分数扩散方程的一些反问题

讨论了具有非局部边界条件族的时间分数扩散方程的两个反问题。在第一个逆问题中，如果最终温度下的数据确定初始分布$吨=吨$给出。当系统的总能量已知时，第二个逆问题解决了源项的时间分量的恢复。函数的双正交系统用于通过傅立叶方法编写级数解。通过使用 Mittag-Leffler 函数的估计并通过对给定数据施加一些规律性条件，建立了这两个逆问题解的经典性质。