Numerical solution of a fractional-order Bagley–Torvik equation by quadratic finite element method

Abstract

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.