- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Advances in Numerical Analysis
Volume 2012 (2012), Article ID 912810, 10 pages
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.
- 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.
- 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.
- 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.
- 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.