Analytical approximate solution of nonlinear dynamic system containing fractional derivative by modified 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 nonlinear dynamic system containing fractional derivative [Ji-zeng Wang et al., Coiflets-based method in the solution of nonlinear dynamic system containing fractional derivative, in: The Fourth International Conference on Nonlinear Mechanics (ICNM-IV), Shanghai, August 2002, pp. 1304–1308] by the relatively new Adomian decomposition method. The results obtained by this method are then graphically represented and then compared with the exact solution. A good agreement of the results is observed.