Identification of time-varying source term in time-fractional diffusion equations

This paper is concerned with the inverse problem of determining time and space dependent source term diffusion equations constant-order time-fractional derivative in $(0,2)$. We examine two different cases. In first one, product spatial temporal terms, we prove that both them can be retrieved by knowledge one arbitrary internal measurement solution for all times. second case, assume varies fixed variable, while a function remaining variables show terms are uniquely determined lateral measurements over entire span. These identification results boil down to weak unique continuation principle case Cauchy data preliminarily established. Finally, numerical reconstruction form carried out through an iterative algorithm based on Tikhonov regularization method.