AN INVERSE TIME-DEPENDENT DIFFUSION COEFFICIENT PROBLEM FOR A SPACE-FRACTIONAL DIFFUSION EQUATION

Space-fractional diffusion equations have recently attracted the attention of many mathematicians from various fields due to their wide-ranging practical applications. This study explores a time-dependent diffusion coefficient in a space-fractional diffusion equation, subject to initial and Dirichlet boundary conditions, along with an overdetermined dataset of integral type, representing time-integrated observations. First, we prove the existence and uniqueness of a weak solution for the direct problem. In the next step, leveraging the overdetermined condition, we refine the solution set of the inverse problem. Finally, under specific assumptions on the available data and by applying Banach's fixed-point theorem, we demonstrate the existence, uniqueness, and stability of the solution.