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Abstract and Applied Analysis
Volume 2014, Article ID 535793, 12 pages
Research Article

Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations

1Department of Mathematics, Jagannath University, Jaipur-303901, Rajasthan, India
2Department of Mathematics, Jagannath Gupta Institute of Engineering and Technology, Jaipur-302022, Rajasthan, India
3Department of Mathematics and Institute for Mathematical Research University Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 16 February 2014; Accepted 8 July 2014; Published 5 August 2014

Academic Editor: Hassan Eltayeb

Copyright © 2014 Jagdev Singh 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 main aim of this work is to present a user friendly numerical algorithm based on homotopy perturbation Sumudu transform method for nonlinear fractional partial differential arising in spatial diffusion of biological populations in animals. The movements are made generally either by mature animals driven out by invaders or by young animals just reaching maturity moving out of their parental territory to establish breeding territory of their own. The homotopy perturbation Sumudu transform method is a combined form of the Sumudu transform method and homotopy perturbation method. The obtained results are compared with Sumudu decomposition method. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and accurate. These results reveal that the proposed method is computationally very attractive.