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Advances in Numerical Analysis
Volume 2012 (2012), Article ID 912810, 10 pages
doi:10.1155/2012/912810
Research Article
Approximation Solution of Fractional Partial Differential Equations by Neural Networks
Department of Mathematics, Faculty of Education, Thamar University, Thamar, Yemen
Received 1 October 2011; Accepted 21 November 2011
Academic Editor: Muhammed I. Syam
Copyright © 2012 Adel A. S. Almarashi. 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.
Linked References
- M. M. Meerschaert and C. Tadjeran, “Finite difference approximations for two-sided space-fractional partial differential equations,” NSFgrant DMC, pp. 563–573, 2004.
- A. S. Chaves, “A fractional diffusion equation to describe Lévy flights,” Physics Letters A, vol. 239, no. 1-2, pp. 13–16, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- D. A. Benson, S. W. Wheatcraft, and M. M. Meerschaert, “The fractional-order governing equation of Levy motion,” Water Resources Research, vol. 36, no. 6, pp. 1413–1423, 2000. View at Publisher · View at Google Scholar
- F. Liu, V. Aon, and I. Turner, “Numerical solution of the fractional advection-dispersion equation,” 2002, http://academic.research.microsoft.com/Publication/3471879.
- K. S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, A Wiley-Interscience Publication, John Wiley & Sons, New York, 1993.
- R. Gorenflo, F. Mainardi, E. Scalas, and M. Raberto, “Fractional calculus and continuous-time finance. III. The diffusion limit,” in Mathematical Finance, Trends Math., pp. 171–180, Birkhäuser, Basel, Switzerland, 2001.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers, Yverdon, Swizerland, 1993.
- G. J. Fix and J. P. Roop, “Least squares finite-element solution of a fractional order two-point boundary value problem,” Computers & Mathematics with Applications, vol. 48, no. 7-8, pp. 1017–1033, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- S. Haykin, Neural Networks, Prntice-Hall, 2006.
- K.-I. Funahashi, “On the approximate realization of continuous mappings by neural networks,” Neural Networks, vol. 2, no. 3, pp. 183–192, 1989.
- A. Al-Marashi and K. Al-Wagih, “Approximation solution of boundary values of partial differential equations by using neural networks,” Thamar University Journal, no. 6, pp. 121–136, 2007.