A Novel Approach for the Analytical Solution of the Fractional Bagley–Torvik Equations

The Bagley–Torvik equations with 1/2 or 3/2 order derivatives describe the motion of real bodies in Newtonian fluids. In this work, we use fractional generalized homotopy analysis method (FGHAM) to determine the solution of inhomogeneous Bagley–Torvik equation of fractional order , which is the particular case of nonlinear fractional differential equation. In application of the method, we take two specific values of the function and exhibit the process. Further, the graphical interpretations are also proposed for the obtained solution.