In this article, we proposed an efficient method to solve the delay Fractional Bagley-Torvik equation. The proposed method is capable of reducing the volume of the computational work as compared to the classical techniques while still maintaining the high accuracy of the numerical result; the size reduction amounts to an improvement of the performance of the approach. Our concern was to provide an analytic solution to the Bagley-Torvik equation using a relatively new analytical technique, the homotopy-Sumudu transformation method. The method does not need to calculate the fractional derivatives or integrations in each term. The results compared with implicit hybrid one-step method yield the efficiency of the presented algorithm. Also, the calculations involved in the method are very simple and straightforward.

在本文中，我们提出了一种有效的方法来求解分数阶Bagley-Torvik方程。与经典技术相比，所提出的方法能够减少计算工作量，同时仍保持数值结果的高精度。尺寸的减小等于方法性能的提高。我们的关注点是使用相对较新的分析技术，即同伦-Sumudu变换方法，为Bagley-Torvik方程提供解析解。该方法不需要计算每个项中的分数导数或积分。将结果与隐式混合一步法进行比较，结果表明了所提算法的有效性。而且，该方法涉及的计算非常简单明了。