On one inverse problem of reconstructing a subdiffusion process with degeneration from nonlocal data

In this article we consider an inverse problem for one-dimensional degenerate fractional heat equation with involution and with periodic boundary conditions with respect to a spatial variable. This problem simulates the process of heat propagation in a thin closed wire wrapped around a weakly permeable insulation. The inverse problem consists in the restoration (simultaneously with the solution) of an unknown right-hand side of the equation, which depends only on the spatial variable. The conditions for redefinition are initial and final states. Existence and uniqueness results for the given problem are obtained via the method of separation of variables.