Existence and regularity in inverse source problem for fractional reaction-subdiffusion equation perturbed by locally Lipschitz sources

<p style='text-indent:20px;'>In this paper, we consider an inverse problem of determining a space-dependent source in the time fractional reaction-subdiffusion equation involving locally Lipschitz perturbations, where additional measurements take place at terminal which are allowed to be nonlinearly dependent on state. By providing regularity estimates both and space resolvent operator using local Hilbert scales, establish some results existence uniqueness solutions type stability solution map under consideration. In addition, when input data more regular values, obtain for direct linear above.</p>