- About this Journal
- Abstracting and Indexing
- 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 780646, 13 pages
Discrete Gamma (Factorial) Function and Its Series in Terms of a Generalized Difference Operator
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.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science Publishers, Yverdon, Switzerland, 1993.
- R. P. Agarwal, Difference Equations and Inequalities, vol. 228, Marcel Dekker, New York, NY, USA, 2nd edition, 2000.
- 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.
- R. L. Magin, Fractional Calculus in Bioengineering, Begell House, 2006.
- 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.
- J. Sabatier, O. P. Agrawal, and J. A. Tenreiro Machado, Advances in Fractional Calculus, Springer, Dordrecht, The Netherlands, 2007.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.