A sideways problem of the time-fractional diffusion equation is investigated. The solution of this problem does not depend on the given data. In view of this, this article uses a Tikhonov-type regularized method to construct an approximate solution and overcome the ill-posedness of considered problem. The a-posteriori convergence estimates of logarithmic and double logarithmic types for the regularized method are derived. Finally, for smooth and non-smooth cases we respectively verify the effectiveness of proposed method by doing the coresponding numerical experiments.

中文翻译：

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Tikhonov型正则化方法求解时间分数阶扩散方程的侧向问题

研究了时间分数扩散方程的侧向问题。该问题的解决方案不依赖于给定的数据。有鉴于此，本文采用了Tikhonov型正则化方法来构造近似解并克服了所考虑问题的不适定性。推导了正则化方法的对数和双对数类型的后验收敛估计。最后，对于平滑和非平滑情况，我们通过进行相应的数值实验分别验证了所提方法的有效性。