Approximate solutions for the Bagley-Torvik fractional equation with boundary conditions using the Polynomial Least Squares Method

Abstract

In this paper we apply the recently introduced Polynomial Least Squares Method (PLSM) to compute approximate analyticalpolynomial solutions for the Bagley-Torvik fractional equation with boundary conditions. The Bagley—Torvik equation may be used to model the motion of real physical systems such as the motion of a thin rigid plate immersed in a Newtonian fluid. In order to emphasize the accuracy of PLSM, we included a comparison with previous approximate solutions obtained for the Bagley-Torvik fractional equation by means of other approximation method.