Solvability of an inverse coefficient problem for a time-fractional diffusion equation with periodic boundary and integral overdetermination conditions

Abstract

This article studies the inverse problem for time-fractional diffusion equations with periodic boundary and integral overdetermination conditions on the rectangular domain. First, we introduce a definition of a classical solution, and then the direct problem is reduced to an equivalent integral equation by the Fourier method. Existence and uniqueness of the solution of the equivalent problem is proved using estimates of the Mittag-Leffer function and generalized singular Gronwall inequalities. In the second part, the inverse problem is considered. This problem reduces to the equivalent integral equation. For solving this equation the contracted mapping principle is applied. The local existence and uniqueness results are proven.