Table of Contents
International Scholarly Research Notices
Volume 2014, Article ID 847419, 12 pages
http://dx.doi.org/10.1155/2014/847419
Research Article

Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations

1Department of Applied Mathematics, Maharaja Agrasen Institute of Technology, Rohini, Delhi 110086, India
2Department of Mathematics and Statistics, Dr. Hari Singh Gaur University, Sagar 470003, India
3Department of Mathematical Sciences, Indian Institute of Technology, Banaras Hindu University, Varanasi 221005, India

Received 29 April 2014; Accepted 27 June 2014; Published 15 October 2014

Academic Editor: S. C. Lim

Copyright © 2014 Vipul K. Baranwal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters and auxiliary functions are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.