Approximate analytical solution for the fractional modified KdV by differential transform method


KURULAY M. , Bayram M.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, vol.15, no.7, pp.1777-1782, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 7
  • Publication Date: 2010
  • Doi Number: 10.1016/j.cnsns.2009.07.014
  • Title of Journal : COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
  • Page Numbers: pp.1777-1782
  • Keywords: Fractional differential equation, Caputo fractional derivative, Differential transform method, fmKdV, fKdV, ADOMIAN DECOMPOSITION METHOD, HOMOTOPY ANALYSIS METHOD, GENERALIZED TAYLORS FORMULA, DIFFUSION-WAVE EQUATION, NUMERICAL-SOLUTIONS, BURGERS EQUATION, ORDER, SYSTEM

Abstract

In this paper, the fractional modified Korteweg-de Vries equation (fmKdV) and fKdV are introduced by fractional derivatives. The approach rest mainly on two-dimensional differential transform method (DTM) which is one of the approximate methods. The method can easily be applied to many problems and is capable of reducing the size of computational work. The fractional derivative is described in the Caputo sense. Some illustrative examples are presented. Crown Copyright (c) 2009 Published by Elsevier B.V. All rights reserved.