标题： 基于次级关系的Caputo分数阶传播子近似及相关数值方法 显示英文标题

标题： Subordination based approximation of Caputo fractional propagator and related numerical methods

摘要： 在这项工作中，我们提出了一种指数收敛的数值方法，用于求解 Caputo 分数阶传播算子 $S_\alpha(t)$ 和与之相关的 Cauchy 问题的温和解，其中包含时间无关的扇形算子系数 $A$ 以及时间上的 Caputo 分数阶导数 $\alpha \in (0,2)$。 所提出的方法通过利用次序原则推广先前开发的 $S_\alpha(t)$ 近似方法而构建。这种方法能够消除误差估计主项对 $\alpha$ 的依赖性，同时保留原始近似方法的其他计算相关特性：对多级并行的支持、处理初始数据时对最小空间光滑性的兼容性，以及对于所有 $t \in [0, T]$ 的稳定指数收敛性。 最终，使用次序原则显著改善了方法的收敛行为，特别是在小参数 $\alpha < 0.5$ 下，并为高效的数据重用开辟了新的机会。 为了验证理论结果，我们考虑了所开发方法在解逼近的正问题和分数阶识别的反问题中的应用。 显示英文摘要

摘要： In this work, we propose an exponentially convergent numerical method for the Caputo fractional propagator $S_\alpha(t)$ and the associated mild solution of the Cauchy problem with time-independent sectorial operator coefficient $A$ and Caputo fractional derivative of order $\alpha \in (0,2)$ in time. The proposed methods are constructed by generalizing the earlier developed approximation of $S_\alpha(t)$ with help of the subordination principle. Such technique permits us to eliminate the dependence of the main part of error estimate on $\alpha$, while preserving other computationally relevant properties of the original approximation: native support for multilevel parallelism, the ability to handle initial data with minimal spatial smoothness, and stable exponential convergence for all $t \in [0, T]$. Ultimately, the use of subordination leads to a significant improvement of the method's convergence behavior, particularly for small $\alpha < 0.5$, and opens up further opportunities for efficient data reuse. To validate theoretical results, we consider applications of the developed methods to the direct problem of solution approximation, as well as to the inverse problem of fractional order identification.