Skip to content
IJPR International Journal of Physical Research E-ISSN 2307-9010

Approximate analytical solution to a time-fractional Zakharov-Kuznetsov equation

Abstract

In this paper we present the approximate analytical solution of a time-fractional Zakharov-Kuznetsov equation via the fractional iteration method. The fractional derivatives are described in the Caputo sense. The approximate results show that the fractional iteration method is a very ecient technique to handle fractional partial differential equations.

Authors and Affiliations

  • Zakia Hammouch FST Errachidia Moulay Ismail University
  • Toufik Mekkaoui FST Errachidia Moulay Ismail University

About this article

Download PDF

References

[1] F. Abidi, K. Omrani: The homotopy analysis method for solving the Fornberg-Whitham equation and comparison with Adomian’s decomposition method, Comput. Math. Appl. 59 (2010) 2743-2750.

[2] J.H. He: Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Engrg. 167 (1998) pp.57-68.

[3] A. Ghorbani: Toward a new analytical method for solving nonlinear fractional differential equations, Comput. Methods Appl. Mech. Engrg. 197 (2008) pp.4173-4179.

[4] M.Shateri and D.D.Ganji: Solitary Wave Solutions for a time-fraction generalized Hirota-Satsuma coupled KdV equation by a new analytical technique, Int.J.Diff.Eqs., 11 pages doi:10.1155/2010/954674.

[5] V.E Zakharov and E.A. Kuznetsov: On three-dimensional solitons, Sov. Phys. JETP 39 (1974), pp.285-286.

View more references (11)

[6] S.Munro and E.J.Parkes: The derivation of a modified Zakharov-Kuznetsov equation and the stability of its solutions. J. of Plasma Phy. 64 (1999), pp.305-317.

[7] K. Batiha: Approximate analytical solution for the Zakharov-Kuznetsov equations with fully nonlinear dispersion, J. Comput. Appl. Math. 216 (2009), pp.157-163.

[8] R.Y.Molliq, M.S.M. Noorani, I. Hashim and R.R. Ahmad: Approximate solutions of fractional Zakharov-Kuznetsov, J. of Comput. and Appl. Maths 233 (2009) pp.103-108. equations by VIM

[9] A.Yildirim and Y.Gulkanat : Analytical Approach to Fractional Zakharov-Kuznetsov Equations by He’s Homotopy Perturbation Method, Commun. Theor. Phys. 53 (2010), pp.1005-1010.

[10] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, CA, 1999.

[11] M. Caputo, Linear models of dissipation whose Q is almost frequency independent, Part II, Geophys. J. R. Astr. Soc. 13 (1967), 529-539.

[12] M. Reed and B. Simon, Methods of Modern Mathematical Physics, I: Functional Analysis, Academic Press, New York, NY, USA, 1980.

[13] S.J. Liao: On the homotopy analysis method for nonlinear problems, Appl. Math. Comput. 147 (2004), pp.499-513.

[14] M. Inc, Exact solutions with solitary patterns for the Zakharov-Kuznetsov equations with fully nonlinear dispersion, Chaos Solitons Fractals 33 (2007) pp.1783-1790.

[15] S. Abbasbandy, E. Shivanian and K. Vajravelu: Mathematical properties of h-curve in the frame work of the homotopy analysis method. Comm. in Nonl. Sci. and Num. Sim., In press, (2011).

[16] Yildiray Keskin, Onur Karaoglu, Sema Servi and Galip Oturanc, The approximate solution of high-order linear fractional differential equations with variable coefficients in terms of generalized Taylor polynomials, Mathematical and Computational Applications, Vol. 16, No. 3, pp. 617-629, 2011.


How to Cite

Hammouch, Z., & Mekkaoui, T. (2013). Approximate analytical solution to a time-fractional Zakharov-Kuznetsov equation. International Journal of Physical Research, 1(2), 28-33. https://doi.org/10.14419/ijpr.v1i2.849