A highly accurate numerical method for solving boundary value problem of generalized Bagley‐Torvik equation

A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space as piecewise polynomials of degree at most and has continuous derivative on the considered domain. Furthermore, under some smoothness, conditions of the exact solution convergence analysis are given. Numerical investigation is carried on several examples, and besides showing the justification of theoretical results, comparisons with existing numerical methods are also given. Results indicate that C‐SM gives highly accurate results and is efficient both in computational time and storage.