Exact Solution of the Bagley-Torvik Equation Using Laplace Transform Method

Abstract

In this paper, the exact solution of the Bagley-Torvik equation which has an important role in fractional order differential equations has been investigated by Laplace transformation method. The Bagley-Torvik equation is transformed into an algebraic equation with Laplace transform. This algebraic equation is solved and the unknown function is found with inverse Laplace transformation. Caputo fractional derivative is considered throughout this work. The examples presented demonstrate the validity and applicability of the Laplace transformation method used to find the exact solution of the Bagley-Torvik equation.