Analytical solution of the generalized Bagley–Torvik equation

In this paper, we investigate the generalized Bagley–Torvik equation with the fractional order \((0,2)\). With a novel max-metric containing a Caputo derivative, the existence and uniqueness of the solution to the initial value problem are derived. We obtain the analytical solutions in terms of the Prabhakar function and the Wiman function, and they expand the well-known results about the general Bagley–Torvik equation. Two examples are presented to illustrate the validity of our main results.