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Analytical and numerical results are reported for an analytical approximate solution of a nonlinear dynamic system containing fractional derivative by a modified decomposition method. Comparison with the exact and numerical solution shows that the present method performs extremely well in terms of accuracy, efficiency and simplicity.
Rocznik
Tom
Strony
1327--1337
Opis fizyczny
Bibliogr. 30 poz., tab., wykr.
Twórcy
autor
autor
autor
- Ranaghat Debnath Institution, Mission Road Ranaghat, PIN --741 201, Nadia, West Bengal, INDIA, tapassut@gmail.com
Bibliografia
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- Abbaoui K. and Cherruault Y. (1995): New ideas for proving convergence of decomposition methods. - Computers Math. Applic., vol.29, No.7, pp.103-108.
- Adomian G. (1989): Nonlinear Stochastic Systems Theory and Applications to Physics.- Netherlands: Kluwer Academic Publishers.
- Adomian G. (1994): Solving Frontier Problems of Physics: The Decomposition Method. - Boston: Kluwer Academic Publishers.
- Cherruault Y. (1989): Convergence of Adomian's method. - Kybernetes, vol.18, pp.3138.
- Datta B.K. (2007): An analysis and estimation of stochastic physical and mechanical systems. - UGC Minor Research Project No. F. PSW/061.
- Datta B.K. (2009): Analytic treatment of time fractional nonlinear operator equation with applications. - Indian Journal of Physics, vol.83, No.9, pp.1315-1322.
- Diethelm K., Ford N.J. and Freed A.D. (2002): A predictor-corrector approach for the numerical solution of fractional differential equations. - Nonlinear Dynamics, vol.29, pp.3-22.
- Glockle W.G. and Nonnenmacher T.F. (1991): Fractional integral operators and foxfunctions in the theory of viscoelasticity. - Macromolecules, vol.24, pp.6426-6434.
- Haldar K. and Datta B.K. (1994): On the approximate solutions of the anharmonic oscillator problem. - International Journal of Mathematical Education in Science and Technology, vol.25, No.6, pp. 907-911.
- Himoun N., Abbaoui K. and Cherruault Y. (1999): New results of convergence of Adomian's method. - Kybernetes, 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, Pt2.
- Kaya D. (2006): The exact and numerical solitary-wave solutions for generalized modified Boussinesq equation. - Physics Letters A, vol.348, No.3-6, pp.244-250.
- Lakshmanan M. (1988): Solitons: Introduction and Applications. - New York: Heidelberg Springer Verlag.
- Miller K.S. and Ross B. (1993): An Introduction to the Fractional Calculus and Fractional Differential Equations. - New York: John Wiley and Sons Inc.
- Ngarhasta N., Some B., Abbaoui K. and Cherruault Y. (2002): New numerical study of Adomian method applied to a diffusion model. - Kybernetes, vol.31, No.1, pp.61-75.
- Odibat Z. and Moman S. (2007): Numerical solution of Fokker-Planck equation with space and time fractional derivatives. - Phys. Lett. A, vol.369, pp.349-358.
- Oldham K.B. and Spanier J. (1974): The Fractional Calculus. - New York and London: Academic Press.
- Podlubny I. (1999): Fractional Differential Equations. - USA, San Diego California: Academic Press.
- Rida S.Z. and Sherbiny H.M. (2008): On the solution of the fractional nonlinear Schrödinger equation . - Phys. Lett. A, vol.372, No.5, pp.553-558.
- 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. - Applied Mathematics and Computation, vol.196, No.1, pp.294-302.
- Seng V., Abbaoui K. and Cherruault Y. (1996): Adomian's polynomials for nonlinear operators. - Mathematical and Computer Modelling, vol.24, No.1, pp.59-65.
- Shawagfeh N.T. (2002): Analytical approximate solutions for nonlinear fractional differential equations. - Appl. Math. and Comp., vol.131, pp.517-529.
- Suarez L.E. and Shokooh A. (1997): An eigenvector expansion method for the solution of motion containing fractional derivatives. - Transaction ASME Journal of Applied Mechanics, vol.64, No.3, pp.629-635.
- 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.
- Tadjeran C., Meerschaert M.M. and Scheffler H. (2006): A second-order accurate numerical approximation for the fractional diffusion equation. - J. Comput. Phys., vol.213, pp.205-213.
- Wang Ji-zeng et al.(2002): Coiflets-based method in the solution of nonlinear dynamic system containing fractional derivative. - The Fourth International Conference on Nonlinear Mechanics (ICNM-IV), Shanghai, pp.1304-1308.
- Wazwaz A.M. (1999): A reliable modification of Adomian decomposition method. - Applied Mathematics and Computation, vol.102, No.1, pp.77-86.
- Wazwaz A.M. (2002): Partial Differential equations: Methods and Applications. - A.A. Balkema Publishers, Lisse, The Netherlands.
- Xingyuan W. and Yijie H. (2008): Projective synchronization of fractional order chaotic system based on linear separation. - Phys. Lett. A., vol.372, No.4, pp.435-441.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BPZ5-0028-0015