Discrete spline methods for solving two point fractional Bagley–Torvik equation

A new discrete spline method is developed to solve the two point fractional Bagley–Torvik equation.The method is based on discrete spline function and a nonstandard Grünwald–Letnikov difference (NSGD) and the weighted and shifted Grünwald–Letnikov difference (WSGD) operators to approximate the fractional derivative. Bounds for Grünwald–Letnikov weights are considered. Convergence analysis is discussed and a class of second order and third order methods are obtained. Illustrative examples are presented to validate the practical usefulness of the methods.