Framelets and their attractive features in many disciplines have attracted a great interest in the recent years. This paper intends to show the advantages of using bi-framelet systems in the context of numerical fractional differential equations (FDEs). We present a computational method based on the quasi-affine bi-framelets with high vanishing moments constructed using the generalized (mixed) oblique extension principle. We use this system for solving some types of FDEs by solving a series of important examples of FDEs related to many mathematical applications. The quasi-affine bi-framelet-based methods for numerical FDEs show the advantages of using sparse matrices and its accuracy in numerical analysis.

中文翻译：

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双框架系统在求解分数阶微分方程中的应用

近年来，Framelet 及其在许多学科中的吸引人的特性引起了极大的兴趣。本文旨在展示在数值分数微分方程 (FDE) 的上下文中使用双框架系统的优势。我们提出了一种基于使用广义（混合）倾斜扩展原理构造的具有高消失矩的准仿射双框架的计算方法。我们通过求解一系列与许多数学应用相关的重要 FDE 示例，使用该系统求解某些类型的 FDE。基于拟仿射双框架的数值 FDE 方法显示了使用稀疏矩阵的优势及其在数值分析中的准确性。