In this paper, we consider a problem of recovering a space-dependent source for a time fractional diffusion wave equation by the fractional Landweber method. The inverse problem has been transformed into an integral equation by using the final measured data. We use the fractional Landweber regularization method for overcoming the ill-posedness. We discuss an a-priori regularization parameter choice rule and an a-posteriori regularization parameter choice rule, and we also prove the conditional stability and convergence rates for the inverse problem. Numerical experiments for four examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed method.

在本文中，我们考虑了通过分数Landweber方法为时间分数扩散波方程恢复空间相关源的问题。通过使用最终的测量数据，反问题已转化为积分方程。我们使用分数的Landweber正则化方法来克服不适。我们讨论了先验正则化参数选择规则和后验正则化参数选择规则，并证明了反问题的条件稳定性和收敛速度。通过一维和二维四个实例的数值实验，证明了该方法的有效性。