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Advances in Numerical Analysis
Volume 2012 (2012), Article ID 780646, 13 pages
doi:10.1155/2012/780646
Research Article

Discrete Gamma (Factorial) Function and Its Series in Terms of a Generalized Difference Operator

G. Britto Antony Xavier, V. Chandrasekar, S. U. Vasanthakumar, and B. Govindan

Department of Mathematics, Sacred Heart College, Tirupattur 635601, India

Received 17 July 2012; Accepted 5 October 2012

Academic Editor: Rüdiger Weiner

Copyright © 2012 G. Britto Antony Xavier 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.

Linked References

  1. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993.
  2. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science Publishers, Yverdon, Switzerland, 1993.
  3. R. P. Agarwal, Difference Equations and Inequalities, vol. 228, Marcel Dekker, New York, NY, USA, 2nd edition, 2000. View at Zentralblatt MATH
  4. R. Almeida and D. F. M. Torres, “Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1490–1500, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. R. L. Magin, Fractional Calculus in Bioengineering, Begell House, 2006.
  6. A. B. Malinowska and D. F. M. Torres, “Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative,” Computers & Mathematics with Applications, vol. 59, no. 9, pp. 3110–3116, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. J. Sabatier, O. P. Agrawal, and J. A. Tenreiro Machado, Advances in Fractional Calculus, Springer, Dordrecht, The Netherlands, 2007. View at Publisher · View at Google Scholar
  8. K. S. Miller and B. Ross, “Fractional difference calculus,” in Univalent Functions, Fractional Calculus, and Their Applications (Koriyama, 1988), pp. 139–152, Horwood, Chichester, UK, 1989. View at Zentralblatt MATH
  9. N. R. O. Bastos, R. A. C. Ferreira, and D. F. M. Torres, “Discrete-time fractional variational problems,” Signal Processing, vol. 91, no. 3, pp. 513–524, 2011.
  10. R. A. C. Ferreira and D. F. M. Torres, “Fractional h-difference equations arising from the calculus of variations,” Applicable Analysis and Discrete Mathematics, vol. 5, no. 1, pp. 110–121, 2011. View at Publisher · View at Google Scholar
  11. G. S. F. Frederico and D. F. M. Torres, “A formulation of Noether's theorem for fractional problems of the calculus of variations,” Journal of Mathematical Analysis and Applications, vol. 334, no. 2, pp. 834–846, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. M. M. Susai Manuel, G. B. A. Xavier, V. Chandrasekar, and R. Pugalarasu, “Theory and application of the generalized difference operator of the nth kind (Part I),” Demonstratio Mathematica, vol. 45, no. 1, pp. 95–106, 2012.
  13. M. M. S. Manuel, G. B. A. Xavier, and E. Thandapani, “Theory of generalised difference operator and its applications,” Far East Journal of Mathematical Sciences (FJMS), vol. 20, no. 2, pp. 163–171, 2006. View at Zentralblatt MATH