Date: 16 Apr 2009

On convergence of homotopy analysis method and its modification for fractional modified KdV equations

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


In this paper, the homotopy analysis method (HAM) and its modification (MHAM) are applied to solve the nonlinear time- and space-fractional modified Korteweg-de Vries (fmKdV). The fractional derivatives are described by Caputo’s sense. Approximate and exact analytical solutions of the fmKdV are obtained. The MHAM in particular overcomes the computing difficulty encountered in HAM. Convergence theorems for both the homogeneous and non-homogeneous cases are given. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the approach.