In this paper, we consider a backward problem for the inhomogeneous time-fractional diffusion equation in a cylinder. Such a problem is ill-posed. Based on the solution given by the separation of variables, we apply a modified fractional Landweber method to solve it. Error estimates are presented under the a-priori and the a-posteriori choice rules for regularization parameters, respectively. Relative to the classical Landweber method, the modified fractional Landweber method can reduce the total number of iterations to achieve the same accuracy. Numerical example is given to show the validity of the scheme.

中文翻译：

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圆柱内非齐次时间分数扩散方程后向问题的修正分数Landweber方法

在本文中，我们考虑圆柱内非齐次时间分数扩散方程的后向问题。这样的问题是不恰当的。基于变量分离给出的解决方案，我们应用改进的分数Landweber方法来解决它。误差估计分别在正则化参数的先验和后验选择规则下呈现。相对于经典的Landweber方法，改进的分数Landweber方法可以减少总迭代次数以达到相同的精度。数值例子说明了该方案的有效性。