Abstract The problem of determining the initial condition from noisy final observations in time-fractional parabolic equations is considered. This problem is well known to be ill-posed, and it is regularized by backward Sobolev-type equations. Error estimates of Hölder type are obtained with a priori and a posteriori regularization parameter choice rules. The proposed regularization method results in a stable noniterative numerical scheme. The theoretical error estimates are confirmed by numerical tests for one- and two-dimensional equations.

中文翻译：

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用 Sobolev 型方程对后向时间分数抛物线方程进行正则化

摘要 考虑了从时间分数抛物线方程中的噪声最终观测确定初始条件的问题。众所周知，这个问题是不适定的，并且通过向后的 Sobolev 型方程正则化。Hölder 类型的误差估计是通过先验和后验正则化参数选择规则获得的。所提出的正则化方法产生稳定的非迭代数值方案。理论误差估计通过一维和二维方程的数值测试得到证实。