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.

中文翻译：

---

通过使用非线性条件在多时分式扩散方程中恢复与时间有关的势函数

在本文中，我们致力于解决非线性逆问题，以便从空间域上积分形式的附加测量中恢复多项时间分数扩散方程中的时间相关势项。首先，我们使用不动点定理研究直接问题解的存在性，唯一性，规则性和稳定性。并且我们得到了与时间相关的逆势项问题的唯一性。在数值上，我们使用Levenberg–Marquardt方法找到近似势函数。给出了四个不同的例子来说明所提方法的可行性和有效性。