International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2528

Full Length Research Paper

Homotopy analysis method with modified Reimann-Liouville derivative for space fractional diffusion equation

Jamshad Ahmad* and Syed Tauseef Mohyud-Din
Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt, Pakistan.
Email: [email protected]

  •  Accepted: 14 November 2013
  •  Published: 23 November 2013

Abstract

In this paper, we applied the homotopy analysis method (HAM) to construct the analytical solutions of the space fractional diffusion equations. The derivatives are defined in the Jumarie’s fractional derivative sense. The explicit solutions of the equations have been presented in the closed form by using initial conditions. Two typical examples have been discussed. The results reveal that the method is very effective and simple. On the basis of computational work and subsequent numerical results, it is worth noting that the advantage of the homotopy analysis methodology is that it displays a fast convergence of the solution.

Key words: Analytical solution, fractional diffusion equation, Reimann-Liouville fractional derivative, homotopy analysis method.