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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 654759, 6 pages
Study on Space-Time Fractional Nonlinear Biological Equation in Radial Symmetry
1Department of Mathematics, Dezhou University, Dezhou 253023, China
2Nonlinear Dynamics and Chaos Group, School of Management, Tianjin University, Tianjin 30072, China
Received 1 September 2012; Revised 24 December 2012; Accepted 25 December 2012
Academic Editor: Clara Ionescu
Copyright © 2013 Yanqin Liu. 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.
- N. Shigesada and K. Kawasaki, Biological Invasions: Theory and Practice, Oxford University, Oxford, UK, 1997.
- S. Petrovskii and N. Shigesada, “Some exact solutions of a generalized Fisher equation related to the problem of biological invasion,” Mathematical Biosciences, vol. 172, no. 2, pp. 73–94, 2001.
- I. Podlubny, Fractional Differential Equations, Academic Press, New York, NY, USA, 1999.
- J. Sabatier, O. P. Agrawal, and J. A. T. Machado, Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, The Netherlands, 2007.
- R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
- J. T. Machado, V. Kiryakova, and F. Mainardi, “Recent history of fractional calculus,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1140–1153, 2011.
- E. K. Lenzi, G. A. Mendes, R. S. Mendes, L. R. Da Silva, and . L. S. Lucena, “Exact solutions to nonlinear nonautonomous space-fractional diffusion equations with absorption,” Physical Review E, vol. 67, no. 51, Article ID 051109, 2003.
- E. K. Lenzi, L. C. Malacarne, R. S. Mendes, and I. T. Pedron, “Anomalous diffsion, nonlinear fractional Fokker-Planck equation and solutions,” Physica A, vol. 319, pp. 245–252, 2003.
- M. Bologna, C. Tsallis, and P. Grigolini, “Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: exact time-dependent solutions,” Physical Review E, vol. 62, no. 2, pp. 2213–2218, 2000.
- C. Tsallis and E. K. Lenzi, “Anomalous diffusion: nonlinear fractional Fokker-Planck equation,” Chemical Physics, vol. 284, pp. 341–347, 2002.
- F. Shakeri and M. Dehghan, “Numerical solution of a biological population model using He's variational iteration method,” Computers & Mathematics with Applications, vol. 54, no. 7-8, pp. 1197–1209, 2007.
- Y. Tan, H. Xu, and S.-J. Liao, “Explicit series solution of travelling waves with a front of Fisher equation,” Chaos, Solitons and Fractals, vol. 31, no. 2, pp. 462–472, 2007.
- A. Kadem and D. Baleanu, “Homotopy perturbation method for the coupled fractional Lotka-Volterra equations,” Romanian Journal of Physics, vol. 56, no. 3-4, pp. 332–338, 2011.
- A. M. A. El-Sayed, S. Z. Rida, and A. A. M. Arafa, “Exact solutions of fractional-order biological population model,” Communications in Theoretical Physics, vol. 52, no. 6, pp. 992–996, 2009.
- A.-M. Wazwaz and A. Gorguis, “An analytic study of Fisher's equation by using Adomian decomposition method,” Applied Mathematics and Computation, vol. 154, no. 3, pp. 609–620, 2004.
- A. K. Najeeb, K. Nasir-Uddin, A. Asmat, and J. Muhammad, “Approximate analytical solutions of fractional reaction-diffusion equations,” Journal of King Saud University, vol. 24, no. 2, pp. 111–118, 2012.
- S. Petrovskii, H. Malchow, and B.-L. Li, “An exact solution of a diffusive predator-prey system,” Proceedings of The Royal Society of London A, vol. 461, no. 2056, pp. 1029–1053, 2005.
- Y. Liu and B. Xin, “Numerical solutions of a fractional predator-prey system,” Advances in Difference Equations, vol. 2011, Article ID 190475, 11 pages, 2011.
- N. A. Khan, M. Ayaz, L. Jin, and A. Yildirim, “On the approximate solutions for the time-fractional reaction-diffusion equation of Fisher type,” International Journal of the Physical Science, vol. 6, pp. 2483–2496, 2011.