Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2748

Full Length Research Paper

Numerical solutions for the nonlinear partial fractional Zakharov-Kuznetsov equations with time and space fractional

Khaled A. Gepreel
  • Khaled A. Gepreel
  • Mathematics Department, Faculty of Science, Zagazig University, Egypt, Mathematics Department, Faculty of Science, Taif University, Saudi Arabia,
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Taher A. Nofal
  • Taher A. Nofal
  • Mathematics Department, Faculty of Science, Taif University, Saudi Arabia, Mathematics Department, Faculty of Science, El-Minia University, Egypt
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Ali A. Al-Thobaiti
  • Ali A. Al-Thobaiti
  • Mathematics Department, Faculty of Science, Taif University, Saudi Arabia
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  •  Received: 08 December 2013
  •  Accepted: 07 June 2014
  •  Published: 15 June 2014

Abstract

In this article, we implement relatively analytical techniques such as the homotopy perturbation method and homotopy analysis method to solve nonlinear partial fractional differential Zakharov-Kuznetsov equations. The fractional derivatives are described in the Caputo sense. We compare between the approximate solutions obtained by the homotopy perturbation method and the approximate solutions obtained by homotopy analysis method. Also we make the figures compare between the approximate solutions. We compare between the approximate solutions and the exact solutions for the partial fractional differential equations when  .
 
Key words: Zakharov-Kuznetsov equations, the fractional derivatives, the homotopy perturbation method, the homotopy perturbation method, the approximate solutions.