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Analytical approximation solution of a mathematical modeling of reaction-diffusion brusselator system by reduced differential transform method | ||
| Journal of Hyperstructures | ||
| دوره 3، شماره 2، اسفند 2014، صفحه 116-125 اصل مقاله (99.34 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2014.2585 | ||
| نویسندگان | ||
| A. Taghavi* 1؛ A. Babaei1؛ A. Mohammadpour2 | ||
| 1Department of Mathematics, University of Mazandaran, P.O.Box 47416-95447, Babolsar, Iran | ||
| 2Department of Mathematics, Babol branch Islamic Azad University , P.O.Box 47471- 37381, Babol, Iran | ||
| چکیده | ||
| In this paper an approximate analytical solution of a mathematical modeling of reaction-diffusion Brusselator system with fractional time derivative will be obtained with the help of the reduced differential transform method. Fractional reactiondiffusion Brusselator system is used for modeling of certain chemical reaction-diffusion processes. The fractional derivatives are described in the Caputo sense. It is indicated that the solutions obtained by the reduced differential transform method are reliable and present an effective method for strongly nonlinear partial equations. | ||
| کلیدواژه‌ها | ||
| Fractional Brusselator system؛ Fractional calculus؛ Reduced differential transform method | ||
| مراجع | ||
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[1] G. Adomian, The Diffusion-Brusselator Equation, Computers Math. Applic., 29 (5) (1995), 1-3. [2] M. Caputo, Linear models of dissipation whose Q is almost frequency indepen-dent, Journal of the Royal Astronomical Society, 13 (1967), 529-539. [3] P. K. Gupta, Approximate analytical solutions of fractional Benney-Lin equation by reduced differential transformmethod and the homotopy perturbation method, Comp. and Math. App. 58 (2011), 28-39. [4] Y. Keskin, G. Oturanc, Reduced Differential Transform Method for Partial Dif-ferential Equations, International Journal of Nonlinear Sciences and Numerical Simulation, 10 (6) (2009), 741-749. [5] Y. Keskin, G. Oturanc, Reduced differential transform method for fractional par-tial differential equations, Nonlinear Sci. Lett. 2 (2010), 61-72. [6] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Frac-tional Differential Equations, Elsevier: Amsterdam (2006). [7] S. Kumar, Y. Khan, A. Yildirim, A mathematical modeling arising in the chem-ical systems and its approximate numerical solution, Asia-Pacific Journal of Chemical Engineering, (2011), doi: 10.1002/apj.647. [8] F. Liu and K. Burrage, Novel techniques in parameter estimation for fractional dynamical models arising from biological systems, Computers Mathematics with Applications, 62 (2011), 822-833. [9] K. S. Millar and B. Ross, An Introduction to the fractional calculus and fractional differential equations, New York: Wiley (1993). [10] S. Momani, Z. Odibat, Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equa-tions, Computers and Mathematics with Applications, 54 (2007), 910-919. [11] Z. Odibat, S. Momani, Approximate solutions for boundary value problems of time-fractional wave equation, Applied Mathematics and Computation, 181 (2006), 767-774. [12] Z. Odibat, S. Momani, Numerical methods for nonlinear partial dierential equa-tions of fractional order, Applied Mathematical Modelling, 32 (2008), 28-39. [13] K.B. Oldham, J. Spanier, The Fractional Calculus, New York: Academic Press (1974). [14] I. Podlubny, Fractional Diferential Equations, vol.198 of Mathematics in Science and Engineering, San Diego: Academic Press (1999). | ||
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