An efficient residual power series method for solving the Bagley-Torvik equation

Abstract

This paper comprehensively analyzes the application of the Residual Power Series (RPS) method to solve the Bagley-Torvik fractional differential equation, originally formulated to model viscoelastic damping in thin plates immersed in Newtonian fluids. The method is rigorously applied to three case studies, with exact solutions verified via analytical methods such as Laplace transforms, demonstrating accuracy for polynomial solutions. Theoretical convergence analysis and numerical validation using MATLAB illustrations demonstrate the efficiency of the RPS as a tool for solving fractional initial value problems.