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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 186934, 7 pages
Research Article

Approximate Analytical Solutions of Fractional Perturbed Diffusion Equation by Reduced Differential Transform Method and the Homotopy Perturbation Method

1Jiangsu Maritime Institute, Nanjing 211100, China
2Institute of Science, PLA University of Science and Technology, Nanjing 211101, China

Received 23 March 2013; Accepted 6 May 2013

Academic Editor: Guanghui Wen

Copyright © 2013 Zhoujin Cui 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.


The approximate analytical solutions of differential equations with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM) and the homotopy perturbation method (HPM). RDTM technique does not require any discretization, linearization, or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology (RDTM) with some known technique (HPM) shows that the present approach is effective and powerful. The numerical calculations are carried out when the initial conditions in the form of periodic functions and the results are depicted through graphs. The two different cases have studied and proved that the method is extremely effective due to its simplistic approach and performance.