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Mathematical Problems in Engineering
Volume 2012, Article ID 502812, 26 pages
http://dx.doi.org/10.1155/2012/502812
Research Article

Fractional Calculus and Shannon Wavelet

Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

Received 18 February 2012; Accepted 13 May 2012

Academic Editor: Cristian Toma

Copyright © 2012 Carlo Cattani. 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. Cattani, “Shannon wavelet analysis,” in Proceedings of the International Conference on Computational Science (ICCS '07), Y. Shi, G. D. van Albada, J. Dongarra, and P. M. A. Sloot, Eds., Lecture Notes in Computer Science, LNCS 4488, Part II, pp. 982–989, Springer, Beijing, China, May 2007.
  2. C. Cattani, “Shannon wavelets theory,” Mathematical Problems in Engineering, vol. 2008, Article ID 164808, 24 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. C. Cattani and J. Rushchitsky, Wavelet and Wave Analysis as applied to Materials with Micro or Nanostructure, vol. 74 of Series on Advances in Mathematics for Applied Sciences, World Scientific Publishing, Singapore, 2007. View at Publisher · View at Google Scholar
  4. I. Daubechies, Ten Lectures on Wavelets, vol. 61 of CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA, 1992. View at Publisher · View at Google Scholar
  5. C. Cattani, “Harmonic wavelet solutions of the Schrödinger equation,” International Journal of Fluid Mechanics Research, vol. 30, no. 5, pp. 463–472, 2003. View at Publisher · View at Google Scholar · View at Scopus
  6. C. Cattani, “Connection coefficients of Shannon wavelets,” Mathematical Modelling and Analysis, vol. 11, no. 2, pp. 117–132, 2006. View at Google Scholar · View at Zentralblatt MATH
  7. C. Cattani, “Shannon wavelets for the solution of integrodifferential equations,” Mathematical Problems in Engineering, vol. 2010, Article ID 408418, 22 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. C. Cattani, “Harmonic wavelets towards the solution of nonlinear PDE,” Computers & Mathematics with Applications, vol. 50, no. 8-9, pp. 1191–1210, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. E. Deriaz, “Shannon wavelet approximation of linear differential operators,” Institute of Mathematics of the Polish Academy of Sciences, no. 676, 2007. View at Google Scholar
  10. A. Latto, H. L. Resnikoff, and E. Tenenbaum, “The evaluation of connection coefficients of compactly supported wavelets,” in Proceedings of the French-USA Workshop on Wavelets and Turbulence, Y. Maday, Ed., pp. 76–89, Springer, 1992.
  11. E. B. Lin and X. Zhou, “Connection coefficients on an interval and wavelet solutions of Burgers equation,” Journal of Computational and Applied Mathematics, vol. 135, no. 1, pp. 63–78, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. J. M. Restrepo and G. K. Leaf, “Wavelet-Galerkin discretization of hyperbolic equations,” Journal of Computational Physics, vol. 122, no. 1, pp. 118–128, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. C. H. Romine and B. W. Peyton, “Computing connection coefficients of compactly supported wavelets on bounded intervals,” Tech. Rep. ORNL/TM-13413, Computer Science and Mathematics Division, Mathematical Sciences Section, Oak Ridge National Laboratory, Oak Ridge, Tenn, USA, 1997. View at Google Scholar
  14. G. Toma, “Specific differential equations for generating pulse sequences,” Mathematical Problems in Engineering, vol. 2010, Article ID 324818, 11 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. C. Toma, “Advanced signal processing and command synthesis for memory-limited complex systems,” Mathematical Problems in Engineering, vol. 2012, Article ID 927821, 13 pages, 2012. View at Publisher · View at Google Scholar
  16. K. B. Oldham and J. Spanier, The Fractional Calculus., Academic Press, London, UK, 1970.
  17. B. Ross, A Brief History and Exposition of the Fundamental Theory of Fractional Calculus, Fractional Calculus and Applications, vol. 457 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1975.
  18. L. B. Eldred, W. P. Baker, and A. N. Palazotto, “Numerical application of fractional derivative model constitutive relations for viscoelastic materials,” Computers and Structures, vol. 60, no. 6, pp. 875–882, 1996. View at Publisher · View at Google Scholar · View at Scopus