About this Journal Submit a Manuscript Table of Contents
International Journal of Differential Equations
Volume 2012 (2012), Article ID 780619, 11 pages
http://dx.doi.org/10.1155/2012/780619
Research Article

Fractional Order Difference Equations

Fluid Dynamics Division, School of Advanced Sciences, VIT University, Tamil Nadu, Vellore 632014, India

Received 11 May 2012; Accepted 17 October 2012

Academic Editor: Shaher Momani

Copyright © 2012 J. Jagan Mohan and G. V. S. R. Deekshitulu. 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

  1. J. B. Diaz and T. J. Osler, “Differences of fractional order,” Mathematics of Computation, vol. 28, pp. 185–202, 1974. View at Zentralblatt MATH
  2. R. Hirota, Lectures on Difference Equations, Science-sha, Tokyo, Japan, 2000.
  3. A. Nagai, “Discrete Mittag-Leffler function and its applications, new developments in the research of integrable systems: continuous, discrete, ultra-discrete,” RIMS Kokyuroku, no. 1302, pp. 1–20, 2003.
  4. G. V. S. R. Deekshitulu and J. J. Mohan, “Fractional difference inequalities,” Communications in Applied Analysis, vol. 14, no. 1, pp. 89–97, 2010. View at Zentralblatt MATH
  5. V. Lakshmikantham, S. Leela, and J. V. Devi, Theory of Fractional Dynamic Systems, CSP, Cambridge, UK, 2009.
  6. V. Lakshmikantham and M. R. M. Rao, Theory of Integro-Differential Equations, vol. 1, Gordon and Breach Science Publishers, Lausanne, The Switzerland, 1995.
  7. H. L. Gray and N. F. Zhang, “On a new definition of the fractional difference,” Mathematics of Computation, vol. 50, no. 182, pp. 513–529, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. G. V. S. R. Deekshitulu and J. J. Mohan, “Some new fractional difference inequalities,” in Proceedings of the International Conference on Mathematical Modelling and Scientific Computation (ICMMSC '12), vol. 283 of Communications in Computer and Information Science, pp. 403–412, Springer-Verlag, Berlin, Heidelberg, 2012.