Exact solutions of coupled burgers equation with time-and space-fractional derivative
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2015-01-24 https://doi.org/10.14419/ijamr.v4i1.4077
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Coupled Burgers Equation with Time and Space-Fractional Derivative the Projected Differential Transforms Method, Numerical Method. -
Abstract
In this paper, He's projected differential transform method (PDTM) has been used to obtain solution nonlinear coupled Burgers equation. This method involves less computational work and can, thus, be easily applied to initial value problems. (PDTM) is used to determine the exact solutions of some nonlinear time and space--fractional partial differential equations. A number of illustrative examples are provided and compared with the other methods. The numerical results obtained by these examples are found to be the same.
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References
[1] Adel Al.rabtah, redat suat Erturk, Shaher Momani: solution of fractional oscillator By using differential transform method. Comp. math. Appli 59 (2010) 1356-1362.
[2] A.M.A. El-Sayed, S.Z. Rida, A.A.M. Arafa, Exact solutions of fractional-order biological population model, Commun. Theor. Phys., 52, pp. 992–996, 2009 http://dx.doi.org/10.1088/0253-6102/52/6/04.
[3] Aydin Secer,Mehmet Ali Akinlar,Adem Cevikel, Efficient solution of system of fractional PDEs by the differential transform method, Advances in differential equations.
[4] Aytac Arikoglu, Ibrahim Ozkol: Solution of fractional differential equations by using differential transform method. Chaos. Solutions . Fractals 34(2007)1473-1481 http://dx.doi.org/10.1016/j.chaos.2006.09.004.
[5] Aytac Arikoglu, Ibrahim Ozkol: Solution of fractional integro – differential equations by using fractional differential transform method. Chaos. Solution. Fractals 40(2009) 251-529.
[6] F. Shakeri, M. Dehghan, Numerical solution of a biological population model using He's variational iteration method, Comput. Math. Appl., 54, pp. 1197–1209, 2007 http://dx.doi.org/10.1016/j.camwa.2006.12.076.
[7] Hüseyin Koçaka, Ahmet Yıldırımb;c, An efficient new iterative method for finding exact solutions of nonlinear time-fractional partial differential equations, Nonlinear Analysis: Modelling and Control, 2011, Vol. 16, No. 4, 403–414.
[8] P. Roul, Numerical solutions of time fractional degenerate parabolic equations by variational iteration method with Jumarie-modified Riemann–Liouville derivative, Math. Methods Appl. Sci., 34(9), pp. 1025–1035, 2011 http://dx.doi.org/10.1002/mma.1418.
[9] Salih M. Elzaki: Exact Solution of the (3+1) dimensional nonlinear Schrodinger equation using differential transform method, International Journal of Applied Mathematical Sciences ISSN 0973-0176 Volume 7, Number 1 (2014), pp. 41-46.
[10] Salih M. Elzaki: Solution of Burger's Equation Using Projected Differential Transform Method, International Journal of Mathematical Sciences, ISSN: 2051-5995, Vol.34, Issue.11498.
[11] Salih M. Elzaki: Exact Solution of Biological Population Model Using Projected Differential Transform Method, International Journal of Mathematical and Computer Modelling, ISSN: 2051- 4271, Vol.19, Issue.11124.
[12] Salih M. Elzaki: Solution of General System of Partial Differential Equation Using Projected Differential Transform Method, International Journal of Applied Mathematics, ISSN: 2051-5227, Vol.29, Issue.1 1271.
[13] Vedat Suat Ertrk. Shaher Momani: Solving systems of fractional differential equations using differential transform method. Journal of Compu. Appli. Math 215 (2008) 142-151. http://dx.doi.org/10.1016/j.cam.2007.03.029.
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How to Cite
Elzaki, S. M. (2015). Exact solutions of coupled burgers equation with time-and space-fractional derivative. International Journal of Applied Mathematical Research, 4(1), 99-105. https://doi.org/10.14419/ijamr.v4i1.4077Received date: 2014-12-26
Accepted date: 2015-01-20
Published date: 2015-01-24