Investigation of inverse problem for unknown coefficient in a time fractional diffusion problem with periodic boundary conditions

This paper is about the identification of time dependent unknown function in a time fractional diffusion problem with periodic boundary conditions. Nonlocal over-determined condition in integral form is taken into account in the determination of unknown function as well as the solution of the problem. The existence, uniqueness as well as continuous dependence on data for the inverse problem is presented with certain regularity and consistency conditions. Generalized Fourier method is utilized in this study. The algorithm of the method and an example are also presented to show the effectiveness and accuracy of the proposed method.