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Zh. Vychisl. Mat. Mat. Fiz., 2016, Volume 56, Number 7, Page 1349 (Mi zvmmf10434)  

This article is cited in 5 scientific papers (total in 5 papers)

Comparison of two reliable analytical methods based on the solutions of fractional coupled Klein–Gordon–Zakharov equations in plasma physics

S. Saha Ray, S. Sahoo

National Institute of Technology, Department of Mathematics, Rourkela-769008, India

Abstract: In this paper, homotopy perturbation transform method and modified homotopy analysis method have been applied to obtain the approximate solutions of the time fractional coupled Klein–Gordon–Zakharov equations. We consider fractional coupled Klein–Gordon–Zakharov equation with appropriate initial values using homotopy perturbation transform method and modified homotopy analysis method. Here we obtain the solution of fractional coupled Klein–Gordon–Zakharov equation, which is obtained by replacing the time derivatives with a fractional derivatives of order $\alpha \in (1, 2], \beta \in (1, 2]$. Through error analysis and numerical simulation, we have compared approximate solutions obtained by two present methods homotopy perturbation transform method and modified homotopy analysis method. The fractional derivatives here are described in Caputo sense.

Key words: fractional coupled Klein–Gordon–Zakharov (KGZ) equation, homotopy perturbation transform method (HPTM), modified homotopy analysis method (MHAM), Caputo Fractional Derivative.

DOI: https://doi.org/10.7868/S0044466916070152

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English version:
Computational Mathematics and Mathematical Physics, 2016, 56:7, 1319–1335

Bibliographic databases:

UDC: 519.634
Received: 28.04.2015
Language:

Citation: S. Saha Ray, S. Sahoo, “Comparison of two reliable analytical methods based on the solutions of fractional coupled Klein–Gordon–Zakharov equations in plasma physics”, Zh. Vychisl. Mat. Mat. Fiz., 56:7 (2016), 1349; Comput. Math. Math. Phys., 56:7 (2016), 1319–1335

Citation in format AMSBIB
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\by S.~Saha~Ray, S.~Sahoo
\paper Comparison of two reliable analytical methods based on the solutions of fractional coupled Klein--Gordon--Zakharov equations in plasma physics
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2016
\vol 56
\issue 7
\pages 1349
\mathnet{http://mi.mathnet.ru/zvmmf10434}
\crossref{https://doi.org/10.7868/S0044466916070152}
\elib{https://elibrary.ru/item.asp?id=26302241}
\transl
\jour Comput. Math. Math. Phys.
\yr 2016
\vol 56
\issue 7
\pages 1319--1335
\crossref{https://doi.org/10.1134/S0965542516070162}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. Baleanu, B. Agheli, M. M. Al Qurashi, “Fractional advection differential equation within caputo and caputo-fabrizio derivatives”, Adv. Mech. Eng., 8:12 (2016), 1687814016683305  crossref  isi  scopus
    2. L. Zou, S. Liang, Ya. Li, D. J. Jeffrey, “Analytic approximations to nonlinear boundary value problems modeling beam-type nano-electromechanical systems”, Z. Naturfors. Sect. A-J. Phys. Sci., 72:3 (2017), 201–206  crossref  isi  scopus
    3. Yu.-Q. Yuan, B. Tian, W.-R. Sun, J. Chai, L. Liu, “Wronskian and Grammian solutions for a $(2+1)$-dimensional Date-Jimbo-Kashiwara-Miwa equation”, Comput. Math. Appl., 74:4 (2017), 873–879  crossref  mathscinet  zmath  isi
    4. Pu J.-C., Hu H.-C., “Exact Solitary Wave Solutions For Two Nonlinear Systems”, Indian J. Phys., 93:2 (2019), 229–234  crossref  isi  scopus
    5. Hendy A.S., Macias-Diaz J.E., “A Numerically Efficient and Conservative Model For a Riesz Space-Fractional Klein-Gordon-Zakharov System”, Commun. Nonlinear Sci. Numer. Simul., 71 (2019), 22–37  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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