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Analytical approximate solution of nonlinear dynamic system containing fractional derivative by modified decomposition method. (English) Zbl 1108.65129

Summary: 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 $P{I}^{\lambda }{D}^{\mu }$ 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 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.

MSC:
 65R20 Integral equations (numerical methods) 45J05 Integro-ordinary differential equations 45G10 Nonsingular nonlinear integral equations 26A33 Fractional derivatives and integrals (real functions)