A Numerical Approach for the Simultaneous Identification of a Source Term and a Robin Boundary Coefficient in Time-Fractional Reaction–Diffusion Equations

In the present study, we develop numerical approaches for the simultaneous determination of a time-dependent right-hand side and a Robin boundary coefficient in linear and quasilinear Caputo time-fractional reaction–diffusion problems based on boundary and interior observations. The well-posedness of the corresponding direct problems is established. A temporal semidiscretization is first constructed using the L 2 − 1 σ scheme, and the solution is decomposed with respect to the unknown functions. The correctness of the proposed method is proved. For the nonlinear diffusion problem, a quasilinearization technique is employed, and the spatial discretization is carried out using finite difference schemes. An iterative procedure is developed to solve the resulting inverse problem. Numerical simulations with noisy data are presented and discussed to demonstrate the efficiency of the method.