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Analytical solution of the Bagley–Torvik equation by Adomian decomposition method. (English) Zbl 1109.65072
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 PI λ D μ 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 and P. J. Torvik, On the appearance of the fractional derivative in the behavior of real materials, ASME J. Appl. Mech., 51, 294–298 (1984); I. Podlubny, Fractional differential equations, Academic Press, San Diego, CA, USA (1999; Zbl 0924.34008)]] 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 (loc. cit.). A good agreement of the results is observed.
MSC:
65L99Numerical methods for ODE