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Discrete Dynamics in Nature and Society
Volume 2012, Article ID 529849, 14 pages
http://dx.doi.org/10.1155/2012/529849
Research Article

Denoising Algorithm Based on Generalized Fractional Integral Operator with Two Parameters

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

Received 23 January 2012; Accepted 21 February 2012

Academic Editor: Garyfalos Papaschinopoulos

Copyright © 2012 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. K. S. Miller and B. Ross, An Introduction to the Fractional Integrals and Derivatives-Theory and Application, John Wiley & Sons, New York, NY, USA, 1993.
  2. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. View at Zentralblatt MATH
  3. R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. B. J. West, M. Bologna, and P. Grigolini, Physics of Fractal Operators, Institute for Nonlinear Science, Springer, New York, NY, USA, 2003. View at Zentralblatt MATH
  5. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. J. Sabatier, O. P. Agrawal, and J. A. T. Machado, Advance in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, The Netherlands, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. A. C. Sparavigna, “Using fractional differentiation in astronomy,” Computer Vision and Pattern Recognition (2010), http://arxiv.org/abs/0910.2381v3.
  8. 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/0910.4637v2.
  9. 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 Scopus
  10. J. A. T. Machado, M. F. Silva, R. S. Barbosa et al., “Some applications of fractional calculus in engineering,” Mathematical Problems in Engineering, vol. 2010, Article ID 639801, 34 pages, 2010. View at Publisher · View at Google Scholar
  11. 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
  12. R. W. Ibrahim and M. Darus, “Subordination and superordination for analytic functions involving fractional integral operator,” Complex Variables and Elliptic Equations. An International Journal of Elliptic Equations and Complex Analysis, vol. 53, no. 11, pp. 1021–1031, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. R. W. Ibrahim and M. Darus, “Subordination and superordination for univalent solutions for fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 345, no. 2, pp. 871–879, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. S. M. Momani and R. W. Ibrahim, “On a fractional integral equation of periodic functions involving Weyl-Riesz operator in Banach algebras,” Journal of Mathematical Analysis and Applications, vol. 339, no. 2, pp. 1210–1219, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. R. W. Ibrahim, “Solutions of fractional diffusion problems,” Electronic Journal of Differential Equations, vol. 2010, no. 147, pp. 1–11, 2010. View at Google Scholar · View at Zentralblatt MATH
  16. R. W. Ibrahim, “On the existence for diffeo-integral inclusion of Sobolev-type of fractional order with applications,” ANZIAM Journal, vol. 52, no. (E), pp. E1–E21, 2010. View at Google Scholar
  17. D. Băleanu, O. G. Mustafa, and R. P. Agarwal, “On the solution set for a class of sequential fractional differential equations,” Journal of Physics A, vol. 43, no. 38, Article ID 385209, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. R. W. Ibrahim and M. Darus, “On analytic functions associated with the Dziok-Srivastava linear operator and Srivastava-Owa fractional integral operator,” Arabian Journal for Science and Engineering, vol. 36, no. 3, pp. 441–450, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. R. W. Ibrahim, “Existence and uniqueness of holomorphic solutions for fractional cauchy problem,” Journal of Mathematical Analysis and Applications, vol. 380, no. 1, pp. 232–240, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science, Yverdon, Switzerland, 1993.
  21. J. T. Machado, V. Kiryakova, and F. Mainardi, “Recent history of fractional calculus,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1140–1153, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. H. M. Srivastava and S. Owa, Univalent Functions, Fractional Calculus, and Their Applications, Ellis Horwood Series: Mathematics and Its Applications, John Wiley & Sons, New York, NY, USA, 1989.
  23. R. W. Ibrahim, “On generalized Srivastava-Owa fractional operators in the unit disk,” Advances in Difference Equations, vol. 2011, article no. 55, 2011. View at Publisher · View at Google Scholar
  24. E. Cuesta, M. Kirane, and S. Malik, “Image structure preserving denoising using generalized fractional time integrals,” Signal Processing, vol. 92, no. 2, pp. 553–563, 2012. View at Publisher · View at Google Scholar