Approximate Analytical Solutions of the Fractional Sharma-Tasso-Olver Equation Using Homotopy Analysis Method and a Comparison with Other Methods

Year 2012, Volume: 9 Issue: 2, - , 01.04.2012

Alaattin Esen Orkun Taşbozan N. Murat Yağmurlu

Abstract

In this paper, the homotopy analysis method (HAM) is successfully applied to
the fractional Sharma-Tasso-Olver equation to obtain its approximate analytical solutions.
Comparison of the obtained results with those of variational iteration method (VIM),
Adomian’s decomposition method (ADM) and homotopy perturbation method (HPM) has
led us to conclude that the method gives significantly important consequences. The HAM
solution includes an auxiliary parameter ~ which provides a convenient way of adjusting
and controlling the convergence region of solution series.

Keywords

Homotopy analysis method, approximate analytical solution, fractional Sharma-Tasso-Olver equation, fractional calculus

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