About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 190726, 17 pages
http://dx.doi.org/10.1155/2012/190726
Research Article

Functions Induced by Iterated Deformed Laguerre Derivative: Analytical and Operational Approach

1Department of Mathematics, Faculty of Electronic Engineering, University of Niš, 18000 Niš, Serbia
2Department of Mathematics, Faculty of Occupational Safety, University of Niš, 18000 Niš, Serbia
3Department of Mathematics, Faculty of Mechanical Engineering, University of Niš, 18000 Niš, Serbia

Received 27 December 2011; Accepted 23 January 2012

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Sladjana D. Marinković 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. C. Tsallis, Introduction to Non-Extensive Statistical Mechanics, Springer, 2009.
  2. L. Nivanen, A. le Méhauté, and Q. A. Wang, “Generalized algebra within a nonextensive statistics,” Reports on Mathematical Physics, vol. 52, no. 3, pp. 437–444, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. G. Kaniadakis, “Statistical mechanics in the context of special relativity,” Physical Review E, vol. 66, no. 5, Article ID 056125, 17 pages, 2002. View at Publisher · View at Google Scholar
  4. G. Kaniadakis, “Maximum entropy principle and power-law tailed distributions,” European Physical Journal B, vol. 70, no. 1, pp. 3–13, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. S. Abe, “Nonextensive statistical mechanics of q-bosons based on the q-deformed entropy,” Physics Letters A, vol. 244, no. 4, pp. 229–236, 1998. View at Publisher · View at Google Scholar
  6. H. Exton, q-Hypergeometric Functions and Applications, Ellis Horwood, Chichester, UK, 1983.
  7. R. Floreanini, J. LeTourneux, and L. Vinet, “More on the q-oscillator algebra and q-orthogonal polynomials,” Journal of Physics A, vol. 28, no. 10, pp. L287–L293, 1995. View at Publisher · View at Google Scholar
  8. M. Stanković, S. Marinković, and P. Rajković, “The deformed exponential functions of two variables in the context of various statistical mechanics,” Applied Mathematics and Computation, vol. 218, no. 6, pp. 2439–2448, 2011. View at Publisher · View at Google Scholar
  9. M. Stanković, S. Marinković, and P. Rajković, “The deformed and modified Mittag-Leffler polynomials,” Mathematical and Computer Modelling, vol. 54, no. 1-2, pp. 721–728, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. M. Aoun, R. Malti, F. Levron, and A. Oustaloup, “Synthesis of fractional Laguerre basis for system approximation,” Automatica A, vol. 43, no. 9, pp. 1640–1648, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. G. Bretti and P. E. Ricci, “Laguerre-type special functions and population dynamics,” Applied Mathematics and Computation, vol. 187, no. 1, pp. 89–100, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. G. Dattoli, M. X. He, and P. E. Ricci, “Eigenfunctions of Laguerre-type operators and generalized evolution problems,” Mathematical and Computer Modelling, vol. 42, no. 11-12, pp. 1263–1268, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. R. S. Johal, “Modified exponential function: the connection between nonextensivity and q-deformation,” Physics Letters A, vol. 258, no. 1, pp. 15–17, 1999. View at Publisher · View at Google Scholar
  14. M. Bohner and A. Peterson, Dynamic Equations on Time Scales, Birkhäauser, Boston, Mass, USA, 2001.
  15. E. Borges, “A possible deformed algebra and calculus inspired in nonextensive thermostatistics,” Physica A, vol. 340, no. 1–3, pp. 95–101, 2004. View at Publisher · View at Google Scholar
  16. Y. B. Cheikh, “Some results on quasi-monomiality,” Applied Mathematics and Computation, vol. 141, no. 1, pp. 63–76, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. G. Szegö, Orthogonal Polynomials, American Mathematical Society, Providence, RI, USA, 4th edition, 1975.
  18. Y. B. Cheikh and H. Chaggara, “Connection problems via lowering operators,” Journal of Computational and Applied Mathematics, vol. 178, no. 1-2, pp. 45–61, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. G. Dattoli, A. Torre, and S. Lorenzutta, “Operational identities and properties of ordinary and generalized special functions,” Journal of Mathematical Analysis and Applications, vol. 236, no. 2, pp. 399–414, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. G. Dattoli, “Operational methods, fractional operators and special polynomials,” Applied Mathematics and Computation, vol. 141, no. 1, pp. 151–159, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH