In this paper, we consider the inverse problem for identifying the source term and the initial value of time-fractional diffusion equation with Caputo-like counterpart hyper-Bessel operator. Firstly, we prove that the problem is ill-posed and give the conditional stability result. Then, we choose the Tikhonov regularization method to solve this ill-posed problem, and give the error estimates under a priori and a posteriori regularization parameter selection rules. Finally, we give numerical examples to illustrate the effectiveness of this method.

中文翻译：

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使用类 Caputo 超贝塞尔算子同时识别时间分数扩散方程的源项和初始值

在本文中，我们考虑用类Caputo对应的超贝塞尔算子来识别时间分数扩散方程的源项和初始值的逆问题。首先，我们证明了该问题的不适定性并给出了条件稳定性结果。然后，我们选择Tikhonov正则化方法来解决这个不适定问题，并给出先验和后验正则化参数选择规则下的误差估计。最后，我们给出数值例子来说明该方法的有效性。