Abstract and Applied Analysis

On Local Fractional Continuous Wavelet Transform

Xiao-Jun Yang, Dumitru Baleanu, H. M. Srivastava, and J. A. Tenreiro Machado

Full-text: Open access

Abstract

We introduce a new wavelet transform within the framework of the local fractional calculus. An illustrative example of local fractional wavelet transform is also presented.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 725416, 5 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393447661

Digital Object Identifier
doi:10.1155/2013/725416

Mathematical Reviews number (MathSciNet)
MR3132565

Citation

Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M.; Tenreiro Machado, J. A. On Local Fractional Continuous Wavelet Transform. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 725416, 5 pages. doi:10.1155/2013/725416. https://projecteuclid.org/euclid.aaa/1393447661


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References

  • I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Transactions on Information Theory, vol. 36, no. 5, pp. 961–1005, 1990.
  • R. K. Martinet, J. Morlet, and A. Grossmann, “Analysis of sound patterns through wavelet transforms,” Journal of Pattern Recognition and Artificial Intelligence, vol. 1, no. 2, pp. 273–302, 1987.
  • C. K. Chui, An Introduction to Wavelets, Academic Press, San Diego, Calif, USA, 1992.
  • L. Debnath, Wavelet Transforms and Their Application, Birkhäuser, Boston, Mass, USA, 2002.
  • C. Cattani, “Harmonic wavelet solution of Poisson's problem,” Balkan Journal of Geometry and its Applications, vol. 13, no. 1, pp. 27–37, 2008.
  • C. Cattani and J. Rushchitsky, Wavelet and Wave Analysis as Applied to Materials with Micro or Nanostructure, World Scientific, 2007.
  • D. Mendlovic, Z. Zalevsky, D. Mas, J. García, and C. Ferreira, “Fractional wavelet transform,” Applied Optics, vol. 36, no. 20, pp. 4801–4806, 1997.
  • L. Chen and D. Zhao, “Optical image encryption based on fractional wavelet transform,” Optics Communications, vol. 254, no. 4–6, pp. 361–367, 2005.
  • E. Dinç, F. Demirkaya, D. Baleanu, Y. Kadio\vglu, and E. Kadio\vglu, “New approach for simultaneous spectral analysis of a complex mixture using the fractional wavelet transform,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 4, pp. 812–818, 2010.
  • E. Dinç and D. Baleanu, “Fractional wavelet transform for the quantitative spectral resolution of the composite signals of the active compounds in a two-component mixture,” Computers & Mathematics with Applications, vol. 59, no. 5, pp. 1701–1708, 2010.
  • E. Dinç, D. Baleanu, and K. Taş, “Fractional wavelet analysis of the composite signals of two-component mixture by multivariate spectral calibration,” Journal of Vibration and Control, vol. 13, no. 9-10, pp. 1283–1290, 2007.
  • J. Shi, N. Zhang, and X. Liu, “A novel fractional wavelet transform and its applications,” Science China Information Sciences, vol. 55, no. 6, pp. 1270–1279, 2012.
  • X. J. Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic publisher, Hong Kong, China, 2011.
  • X. J. Yang, D. Baleanu, and J. T. A. Machado, “Mathematical aspects of Heisenberg uncertainty principle within local fractional Fourier analysis,” Boundary Value Problems, vol. 2013, no. 1, article 131, 2013.
  • X. J. Yang and D. Baleanu, “Fractal heat conduction problem solved by local fractional variation iteration method,” Thermal Science, vol. 17, no. 2, pp. 625–628, 2013.
  • A.-M. Yang, X.-J. Yang, and Z.-B. Li, “Local fractional series expansion method for solving wave and diffusion equations on Cantor sets,” Abstract and Applied Analysis, vol. 2013, Article ID 351057, 5 pages, 2013.
  • W.-H. Su, D. Baleanu, X.-J. Yang, and H. Jafari, “Damped wave equation and dissipative wave equation in fractal strings within the local fractional variational iteration method,” Fixed Point Theory and Applications, vol. 2013, article 89, 2013.
  • X. J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science, New York, NY, USA, 2012.
  • A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204, Elsevier Science, Amsterdam, The Netherlands, 2006.