The diffusion equation has many applications in fields such as physics, environment, and fluid mechanics. In this paper, we consider the problem of identifying an unknown source for a time-fractional diffusion equation in a general bounded domain from the nonlocal integral condition. The problem is non-well-posed in the sense of Hadamard, i.e, if the problem has only one solution, the solution will not depend continuously on the input data. To get a stable solution and approximation, we need to offer the regularization methods. The first contribution to the paper is to provide a regularized solution using the modified fractional Landweber method. Two choices are proposed including a priori and a posteriori parameter choice rules, to estimate the convergence rate of the regularized methods. The second new contribution is to use truncation to give an estimate of \(L^p\) for the convergence rate.

扩散方程在物理学、环境和流体力学等领域有很多应用。在本文中，我们考虑从非局部积分条件识别一般有界域中时间分数扩散方程的未知来源的问题。该问题在 Hadamard 意义上是非适定的，即如果问题只有一个解，则该解将不会连续依赖于输入数据。为了获得稳定的解和近似值，我们需要提供正则化方法。该论文的第一个贡献是使用改进的分数 Landweber 方法提供了一个正则化的解决方案。提出了两种选择，包括先验和后验参数选择规则，以估计正则化方法的收敛速度。\(L^p\)为收敛速度。