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Nonperturbative analytical solution of the time fractional advection problem

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Języki publikacji
EN
Abstrakty
EN
A nonperturbative analytic solution is derived for the time fractional nonlinear advection problem by using Adomian's Decomposition Method (ADM). The solution is obtained in the form of a power series with easily computable coefficients. The present method performs extremely well in terms of accuracy, efficiency and simplicity.
Rocznik
Strony
629--636
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
autor
autor
  • Department of Mathematics, Ranaghat Debnath Institution Mission Road, Ranaghat - 741202, Nadia, W.B. INDIA, tapassut@gmail.com
Bibliografia
  • Abbaoui K. and Cherruault Y. (1994): Convergence of Adomian's Method Applied to Differential Equations - Comput. Math. Appl., vol.28, No.5, pp.103-109.
  • Adomian G. (1994): Solving Frontier Problems of Physics: The Decomposition Method. - Boston: Kluwer Academic Publishers.
  • Agarwal O.P. (2002): Solution for a fractional diffusion-wave equation defined in a bounded domain. - Nonlinear Dynamics, vol.29, pp.145-155.
  • Cherruaut Y. (1989): Convergence of Adomian's Method. - Kybernets, vol.18, pp.31-38.
  • Das S. (2008): - Functional Fractional Calculus. - Heidelberg: Springer Verlag.
  • Datta B.K. (2009): Analytic treatment of time fractional nonlinear operator equation with applications. - Indian Jr. of Physics, vol.83, No.9, pp.1315-1322.
  • Dehgan M. and Shokri A. (2007): A numerical method for two-dimensional Schrödinger equation using collocation and radial basis functions. - Comput. Math. Appl., vol.54, No.1, pp.136-146.
  • Himoun N., Abbaoui K. and Cherruault Y. (1999): New results of convergence of Adomian's method. - Kybernets, vol.28, No.4-5, pp.423-429.
  • Jiang K. (2005): Multiplicity of nonlinear thermal convection in a spherical shell. - Phys. Rev. E., Stat Nonlinear Soft Matter Phys., vol.71, No.1 Pt 2.
  • Kaya D. (2006): The exact and numerical solitary-wave solutions for generalized modified Boussinesq equation. - Physics Letters A, vol.348(3-6), pp.244-250.
  • Lakshmanan M. (1988): - Solitons : Introduction and Applications. - New York: Heidelberg: Springer Verlag.
  • Mainardi F., Raberto M., Gorenflo R. and Scalas E. (2000): Fractional calculus and continuous-time finance II: the waiting-time distribution. - Physica A, vol.287, pp.468-481.
  • Meerschaert M.M., Scheffler H. and Tadjeran C. (2006): Finite difference methods for two-dimensional fractional dispersion equation. - Jr. Comput. Phys., vol.211, pp.249-261.
  • Miller K.S. and Ross B. (1993): - An Introduction to the Fractional Calculus and Fractional Differential Equations. - New York: John Wiley and Sons.
  • Ngarhasta N., Some B., Abbaoui K. and Cherruault Y. (2002): New numerical study of Adomian method applied to a diffusion model. - Kybernets, vol.31, No.1, pp.61-75.
  • Odibat Z. and Momani S. (2007): Numerical solution of Fokker-Planck equation with space and time-fractional derivatives. - Phys. Lett. A, vol.369, pp.349-358.
  • Podlubny I. (1999): - Fractional Differential Equations - San Diego, California, US: Academic Press.
  • Riewe F. (1997): Mechanics with fractional derivatives. - Phys. Rev. E, vol.55, No.3, pp.3581-3591.
  • Roberto M., Scalas E. and Mainardi F. (2002): Waiting-times and returns in high-frequency financial data: an empirical study. - Physica A, vol.314, pp.749-755.
  • Saha Ray S., Chaudhuri K.S. and Bera R.K. (2008): Application of modified decomposition method for the analytical solution of space fractional diffusion equation. - Appl. Math. Comput., vol.196, No.1, pp.294-302.
  • Shawagfeh N.T. (2002): Analytical approximate solutions for nonlinear fractional differential equations. - Applied Math. and Comput., vol.131, pp.517-529.
  • Sutradhar T. (2009): Nonperturbative analytical solution of the time fractional nonlinear Burger's equation. - Indian Journal of Physics,vol.83, No.12, pp.1681-1690.
  • Waswas A.M. (2002): - Partial Differential Equations: Methods and Applications. - A. A. Balkema Publishers, Lisse, The Netherlands.
  • Xinguam W. and He Yijie (2008): Projective synchronization of fractional order chaotic system based on linear separation. - Phys. Lett. A372, vol.4, pp.435-441.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ5-0027-0018
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