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

In this paper, we deal with a nonlinear inverse problem for recovering a time-dependent potential term in a time fractional diffusion equation from an additional measurement in the form of integral over the space domain. By using the fixed point theorem, the existence, uniqueness, regularity and stability of the direct problem are proved. The uniqueness of the inverse problem is proved by the property of Caputo fractional derivative. Numerically, we employ the Levenberg-Marquardt method to find the approximate potential function. Some different type examples are presented to show the feasibility and efficiency of the proposed method.

Automated summary

This paper deals with a nonlinear inverse problem for recovering a time-dependent potential term in a time fractional diffusion equation from an additional measurement in the form of integral over the space domain. By using the fixed point theorem, the existence, uniqueness, regularity, and stability of the direct problem are proved. The uniqueness of the inverse problem is proved by the property of Caputo fractional derivative, and the Levenberg-Marquardt method is employed for numerical approximation. The feasibility and efficiency of the proposed method are demonstrated through various examples.