Multiple Terms Identification of Time Fractional Diffusion Equation with Symmetric Potential from Nonlocal Observation

This paper considers a simultaneous identification problem of a time-fractional diffusion equation with a symmetric potential, which aims to identify the fractional order, the potential function, and the Robin coefficient from a nonlocal observation. Firstly, the existence and uniqueness of the weak solution are established for the forward problem. Then, by the asymptotic behavior of the Mittag-Leffler function, the Laplace transform, and the analytic continuation theory, the uniqueness of the simultaneous identification problem is proved under some appropriate assumptions. Finally, the Levenberg–Marquardt method is employed to solve the simultaneous identification problem for finding stably approximate solutions of the fractional order, the potential function, and the Robin coefficient. Numerical experiments for three test cases are given to demonstrate the effectiveness of the presented inversion method.