Computational Relationship of The Surface Area and Stiffness of the Spring Constant on Fractional Bagley-Torvik Equation

Abstract

In this paper, we formulate an efficient algorithm based on a new iterative method for the numerical solution of the Bagley-Torvik equation. The fractional differential equation arises in many areas of applied mathematics including viscoelasticity problems and applied mechanics of the oscillation process. We construct the fractional derivatives via the Caputo-type fractional operator to formulate a three-step algorithm using the MAPLE 18 software package. We further investigate the relationships between the surface area and stiffness of the spring constants of the Bagley-Torvik equation on three case problems and numerical results are presented to demonstrate the efficiency of the proposed algorithm.