Stability and regularity in inverse source problem for generalized subdiffusion equation perturbed by locally Lipschitz sources

In this paper, we investigate an inverse problem of recovering a space-dependent source in the generalized subdiffusion equation involving locally Lipschitz perturbations, where the additional observations take place at the terminal time and are allowed to be nonlinearly dependent on the state. By using the theory of completely positive functions and local estimates on Hilbert scales, we establish some results on the existence, uniqueness and the Lipschitz-type stability of the solution map of the problem under consideration. In addition, when the input data take more regular values, we obtain results on regularity in time of solution for both the direct linear problem and the inverse problem above.