Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley–Torvik differential equation

Abstract

The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley–Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams–Bashforth–Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.