In this paper, a fast multiscale Galerkin algorithm is developed for solving the boundary value problem of the fractional Bagley–Torvik equation. For this purpose, we employ multiscale orthogonal functions having vanishing moments as the basis of the trial space, and we propose a truncation strategy for the coefficient matrix of the corresponding discrete system which leads to a fast algorithm. We show the algorithm has nearly linear computational complexity (up to a logarithmic factor). Numerical experiments are presented to illustrate the efficiency, accuracy and convergence of the proposed algorithm. Also, comparisons with some other existing methods are made to confirm the reliability of the algorithm

中文翻译：

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快速多尺度Galerkin算法，求解分数阶Bagley-Torvik方程的边值问题

在本文中，开发了一种快速的多尺度Galerkin算法来解决分数阶Bagley-Torvik方程的边值问题。为此，我们采用具有消失矩的多尺度正交函数作为试验空间的基础，并针对相应离散系统的系数矩阵提出了一种截断策略，从而提出了一种快速算法。我们证明了该算法具有近乎线性的计算复杂度（高达对数因子）。数值实验表明了该算法的有效性，准确性和收敛性。此外，与其他一些现有方法进行了比较，以确认算法的可靠性