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Application of Adomian Decomposition Method and Variational Iteration Method for the solution of fractional Basset differential equation

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EN
In this paper, the Adomian decomposition method (ADM) and variational iteration method (VIM) are implemented to obtain an approximate solution for a fractional Basset equation with an arbitrary order […].The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. The approximate solution obtained using the VIM is exactly the same and in good agreement to that obtained by using the ADM.
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1163--1167
Opis fizyczny
Bibliogr. 10 poz., wykr.
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Bibliografia
  • Adomian G. (1994): Solving Frontier Problems of Physics: The Decomposition Method. - Boston: Kluwer Academic Publishers.
  • Diethelm K. and Ford N.J. (2002): Numerical solution of the Bagley-Torvik equation. - BIT, vol.42, pp.490-507.
  • Diethelm K. and Ford N.J. (2001): The numerical solution of linear and non-linear fractional differential equations involving fractional derivatives several of several orders. - Numerical Analysis Report 379, Manchester Center for Numerical Computational Mathematics.
  • He J.H. (1998): Approximate analytical solution for seepage flow with fractional derivatives in porous media. - Comput. Methods Appl. Mech. Eng., vol.167, pp.57-68.
  • He J.H. (1999): Variational iteration method- a kind of non-linear analytical technique: some examples. - Int. J. Nonlinear Mech., vol.34, pp.699-708.
  • Mainardi F. (1997): Some basic problems in continuum and statistical mechanics, In: A. Carpinteri and F. Mainardi (Eds). - Fractals and Fractional Calculus in Continuum Mechanics, Springer, pp.291-348, Wien.
  • Podlubny I. (1999): Fractional Differential Equations. - Academic Press.
  • Saha Ray S. and Bera R.K. (2005): Analytical solution of a dynamic system containing fractional derivative of order one-half by Adomian Decomposition Method. - Journal of Applied Mechanics, vol.72, No.2, pp.290-295.
  • Saha Ray S. and Bera R.K. (2005): An approximate solution of a nonlinear fractional differential equation by adomian decomposition method. - Applied Mathematics and Computation, vol.167, pp.561-571.
  • Saha Ray S. and Bera R.K. (2005): Analytical solution of the Bagley Torvik equation by Adomian decomposition method. - Appl. Math. Comput., vol.168, No.1, pp.398-410.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ5-0003-0016
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