Explicit Solution for the Bagley–Torvik Equation With Variable Coefficients

ABSTRACT Analytical solutions to the Bagley–Torvik equation with variable coefficients are difficult to be obtained, so most previous research focused on numerical solutions. In this paper, with the help of a fractional integral equation, we obtain an explicit representation of a unique exact solution of the initial value problem for the Bagley–Torvik equation with variable coefficients in a weighted space. We present three examples and give numerical simulations as an application.