Recovering a time-dependent potential function in a multi-term time fractional diffusion equation by using a nonlinear condition

In the present paper, we devote our effort to a nonlinear inverse problem for recovering a time-dependent potential term in a multi-term time fractional diffusion equation from an additional measurement in the form of an integral over the space domain. First we study the existence, uniqueness, regularity and stability of the solution for the direct problem by using the fixed point theorem. And we obtain the uniqueness of the inverse time-dependent potential term problem. Numerically, we use the Levenberg-Marquardt method to find the approximate potential function. Four different examples are presented to show the feasibility and efficiency of the proposed method.