Restoration of an solution's initial data and a source of the fractional diffusion equation in the space of periodic distributions

Анотація

We prove the correctness of an inverse problem for a time fractional sub-diffusion equation. This problem is to find a solution of direct problem, which is classical in time with values in the space of periodic spatial distributions, its initial data and a source term of the equation. We show that the same kind time integral over-determination conditions may be used.