Variational iteration method for the time-fractional Fornberg-Whitham equation


Sakar M. G. , Erdoğan F., YILDIRIM A.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol.63, no.9, pp.1382-1388, 2012 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 63 Issue: 9
  • Publication Date: 2012
  • Doi Number: 10.1016/j.camwa.2012.01.031
  • Journal Name: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1382-1388
  • Keywords: Variational iteration method, Fractional Fornberg-Whitham equation, Caputo derivative, Approximate solution, Lagrange multiplier, PARTIAL-DIFFERENTIAL-EQUATIONS, APPROXIMATE ANALYTICAL SOLUTION, HOMOTOPY ANALYSIS METHOD, FLUID

Abstract

This paper presents the approximate analytical solutions to solve the nonlinear Fornberg–Whitham equation with fractional time derivative. By using initial values, explicit solutions of the equations are solved by using a reliable algorithm like the variational iteration method. The fractional derivatives are taken in the Caputo sense. The present method performs extremely well in terms of efficiency and simplicity. Numerical results for different particular cases of αα are presented graphically.

This paper presents the approximate analytical solutions to solve the nonlinear Fornberg-Whitham equation with fractional time derivative. By using initial values, explicit solutions of the equations are solved by using a reliable algorithm like the variational iteration method. The fractional derivatives are taken in the Caputo sense. The present method performs extremely well in terms of efficiency and simplicity. Numerical results for different particular cases of a are presented graphically. (c) 2012 Elsevier Ltd. All rights reserved.