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 time fractional variant Bussinesq equation by homotopy analysis method

Mohamed S. Mohamed1,2  and  Khaled A. Gepreel1,3*
¹Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia. 2Mathematics Department, Faculty of Science, Al-Azhar University, Cairo, Egypt . 3Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt.
Email: [email protected], [email protected]

  •  Accepted: 06 November 2013
  •  Published: 25 November 2013

Abstract

In this article, the fractional derivatives in the sense of Caputo, and the homotopy analysis method (HAM) are used to construct the approximate solutions for the nonlinear fractional variant Bussinesq equations with respect to time fractional derivative. The HAM contains a certain auxiliary h parameter which provides us a simple way to adjust and control the convergence region and rate of convergence of the series solution. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equation.

Key words: Fractional calculus, homotopy analysis method, Caputo's fractional derivative, fractional variant Bussinesq equation.

Abbreviation

FDEs, Fractional differential equations; HPM, homotopy-perturbation method; HAM, homotopy analysis method.