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


DOI: 10.1007/s12190-009-0274-1

Cite this article as:
Abdulaziz, O., Bataineh, A.S. & Hashim, I. J. Appl. Math. Comput. (2010) 33: 61. doi:10.1007/s12190-009-0274-1


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.


Fractional modified Korteweg-de Vries Homotopy analysis method Caputo’s fractional derivative 

Mathematics Subject Classification (2000)

35Q53 41A58 

Copyright information

© Korean Society for Computational and Applied Mathematics 2009

Authors and Affiliations

  1. 1.School of Mathematical Sciences, Faculty of Science and TechnologyUniversity Kebangsaan MalaysiaBangi SelangorMalaysia