Improved Numerical Approach for Bagley–Torvik Equation Using Fractional Integral Formula and Adams–Moulton Method

Abstract

In this paper, we introduce a numerical technique for solving Bagley–Torvik equations which plays an outstanding role in fractional calculus. To handle the derivatives and fractional integral in the Bagley–Torvik equations, the Laplace transform is employed to convert the equations to fractional integration equations. The resulting integral equations are solved by implicit Adams–Moulton methods. Moreover, we show the analytic convergence order of the proposed technique through the convergence analysis, and the analysis is validated by the numerical experiments. Illustrative experiments also demonstrate the validity and efficiency of the proposed method by comparing it with other existing methods.