Analytical solution of the Bagley Torvik equation by Adomian decomposition method

摘要

The fractional derivative has been occurring in many physical problems such as frequency dependent damping behavior of materials, motion of a large thin plate in a Newtonian fluid, creep and relaxation functions for viscoelastic materials, the PIλDμ controller for the control of dynamical systems, etc. Phenomena in electromagnetics, acoustics, viscoelasticity, electrochemistry and material science are also described by differential equations of fractional order. The solution of the differential equation containing fractional derivative is much involved. Instead of application of the existing methods, an attempt has been made in the present analysis to obtain the solution of Bagley–Torvik equation [R.L. Bagley, P.J. Torvik, On the appearance of the fractional derivative in the behavior of real materials, ASME J. Appl. Mech., 51 (1984) 294–298; I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, CA, USA, 1999] by the relatively new Adomian decomposition method. The results obtained by this method are then graphically represented and then compared with those available in the work of Podlubny [I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, CA, USA, 1999]. A good agreement of the results is observed.