In this paper, we consider an inverse source problem for fractional diffusion equation with Riemann–Liouville derivative. The considered problem is ill-posed, i.e., the solution does not depend continuously on the given data. We assume the solutions of the equation can be represented by a Fourier series. The Tikhonov regularization method is applied to solve this problem. In the theoretical results, the convergence estimates between the exact solutions and the regularized solutions are presented under a priori and a posteriori parameter choice rules.

中文翻译：

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Riemann-Liouville导数分数阶扩散方程的反源问题正则化

在本文中，我们考虑使用Riemann-Liouville导数的分数阶扩散方程的逆源问题。所考虑的问题是不适当的，即解决方案并不连续依赖于给定的数据。我们假设方程的解可以用傅立叶级数表示。Tikhonov正则化方法用于解决此问题。在理论结果中，在先验和后验参数选择规则下给出了精确解和正则解之间的收敛估计。