Table of Contents
ISRN Mathematical Physics
Volume 2012, Article ID 197068, 11 pages
http://dx.doi.org/10.5402/2012/197068
Research Article

Approximate Solutions to Time-Fractional Schrödinger Equation via Homotopy Analysis Method

1Department of Mathematics, University of Karachi, Karachi 75270, Pakistan
2Abdul Salam School of Mathematical Sciences, GC University, Lahore, Pakistan
3Department of Mathematics, NED University of Engineering and Technology, Karachi 75270, Pakistan

Received 21 October 2011; Accepted 13 November 2011

Academic Editors: P. Roy and W.-H. Steeb

Copyright © 2012 Najeeb Alam Khan 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 construct the approximate solutions of the time-fractional Schrödinger equations, with zero and nonzero trapping potential, by homotopy analysis method (HAM). The fractional derivatives, in the Caputo sense, are used. The method is capable of reducing the size of calculations and handles nonlinear-coupled equations in a direct manner. The results show that HAM is more promising, convenient, efficient and less computational than differential transform method (DTM), and easy to apply in spaces of higher dimensions as well.