About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 795954, 7 pages
http://dx.doi.org/10.1155/2013/795954
Research Article

On Generalized Fractional Differentiator Signals

1Faculty of Computer Science and Information Technology, University Malaya, 50603 Kuala Lumpur, Malaysia
2Institute of Mathematical Sciences, University Malaya, 50603 Kuala Lumpur, Malaysia

Received 17 January 2013; Accepted 16 March 2013

Academic Editor: Jehad Alzabut

Copyright © 2013 Hamid A. Jalab and Rabha W. Ibrahim. 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. A. C. Sparavigna, “Using fractional differentiation in astronomy, Computer Vision and Pattern Recognition,” 2010, http://arxiv.org/abs/0910. 2381.
  2. R. Marazzato and A. C. Sparavigna, “Astronomical image processing based on fractional calculus: the AstroFracTool, Instrumentation and Methods for Astrophysics,” 2009, http://arxiv.org/abs/0910. 4637.
  3. H. B. Kekre, S. D. Thepade, and A. Maloo, “Image retrieval using fractional coefficients of transformed image using DCT and Walsh transform,” International Journal of Engineering Science and Technology, vol. 2, pp. 362–371, 2010.
  4. C. C. Tseng, “Design of variable and adaptive fractional order FIR differentiators,” Signal Processing, vol. 86, no. 10, pp. 2554–2566, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. J. Hu, Y. Pu, and J. Zhou, “A novel image denoising algorithm based on riemann-liouville definition,” Journal of Computers, vol. 6, no. 7, pp. 1332–1338, 2011. View at Publisher · View at Google Scholar · View at Scopus
  6. R. W. Schafer, “What is a savitzky-golay filter?” IEEE Signal Processing Magazine, vol. 28, no. 4, pp. 111–117, 2011. View at Publisher · View at Google Scholar · View at Scopus
  7. H. A. Jalab and R. W. Ibrahim, “Denoising algorithm based on generalized fractional integral operator with two parameters,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 529849, 15 pages, 2012. View at Zentralblatt MATH · View at MathSciNet
  8. H. A. Jalab and R. W. Ibrahim, “Texture enhancement for medical images based on fractional differential mask,” Discrete Dynamics in Nature and Society, vol. 2013, Article ID 618536, 14 pages, 2013.
  9. H. A. Jalab and R. W. Ibrahim, “Texture enhancement based on the Savitzky-Golay fractional differential operator,” Mathematical Problems in Engineering, vol. 2013, Article ID 149289, 8 pages, 2013.
  10. S. Samadi, M. O. Ahmad, and M. N. S. Swamy, “Exact fractional-order differentiators for polynomial signals,” IEEE Signal Processing Letters, vol. 11, no. 6, pp. 529–532, 2004. View at Publisher · View at Google Scholar · View at Scopus
  11. S. C. Dutta Roy and B. Kumar, Digital Differentiators, North Holand, Amsterdam, The Netherlands, 1993.
  12. H. M. Srivastava and S. Owa, Univalent Functions, Fractional Calculus, and Their Applications, Halsted Press, John Wiley and Sons, New York, NY, USA, 1989.
  13. R. W. Ibrahim, “On generalized Srivastava-Owa fractional operators in the unit disk,” Advances in Difference Equations, vol. 2011, article 55, 10 pages, 2011. View at MathSciNet