The fractional-order Bagley–Torvik equation has many applications in the field of life science and engineering. In this paper, we develop a new scheme based on the existing finite element method for the numerical solution of the Bagley–Torvik equation of order (0, 2). We adopt the formulation of the equation in a simple and generalized way. The existence and uniqueness of the solution and its error estimations are derived based on the technique we derived. A series of numerical examples are provided to demonstrate the accuracy, efficiency, and simplicity of the method. The results are depicted graphically and in a table to compare the exact and approximate solutions obtained by following the numerical methods available in the literature. The numerical experiment shows that using a small number of quadratic functions, the accuracy of our numerical technique is better than the existing methods. Since the Bagley–Torvik equation represents the general form of fractional-order boundary value problems, the numerical technique indicates the identical path to solve the similar type of the fractional-order boundary value problems.

分数阶Bagley–Torvik方程在生命科学和工程领域具有许多应用。在本文中，我们基于现有的有限元方法开发了一种新的方案，用于求解Bagley–Torvik阶方程（0，2）的数值解。我们以一种简单而通用的方式采用方程式。解决方案的存在和唯一性及其误差估计是基于我们得出的技术得出的。提供了一系列数值示例，以演示该方法的准确性，效率和简便性。结果以图形方式显示在表格中，以比较通过遵循文献中可用的数值方法获得的精确解和近似解。数值实验表明，使用少量的二次函数，我们的数值技术的准确性优于现有方法。由于Bagley–Torvik方程表示分数阶边值问题的一般形式，因此数值技术指出了解决相似类型的分数阶边值问题的相同路径。