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International Journal of Differential Equations
Volume 2010 (2010), Article ID 968186, 13 pages
The Use of Fractional B-Splines Wavelets in Multiterms Fractional Ordinary Differential Equations
School of Mathematical and Computer Sciences, Fuzhou University, Fuzhou 350002, China
Received 31 July 2009; Revised 2 November 2009; Accepted 4 November 2009
Academic Editor: Fawang Liu
Copyright © 2010 X. Huang and X. Lu. 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.
- P. Kumar and O. P. Agrawal, “Numerical scheme for the solution of fractional differential equations of order greater than one,” Journal of Computational and Nonlinear Dynamics, vol. 1, no. 2, 8 pages, 2006.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication, John Wiley & Sons, New York, NY, USA, 1993.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- J. T. Edwards, N. J. Ford, and A. C. Simpson, “The numerical solution of linear multi-term fractional differential equations; systems of equations,” Journal of Computational and Applied Mathematics, vol. 148, no. 2, pp. 401–418, 2002.
- K. Diethelm and N. J. Ford, “Analysis of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 265, no. 2, pp. 229–248, 2002.
- K. Diethelm, N. J. Ford, and A. D. Freed, “A predictor-corrector approach for the numerical solution of fractional differential equations,” Nonlinear Dynamics, vol. 29, no. 1–4, pp. 3–22, 2002.
- K. Diethelm, “Efficient solution of multi-term fractional differential equations using methods,” Computing, vol. 71, no. 4, pp. 305–319, 2003.
- C. Yang and F. Liu, “A computationally effective predictor-corrector method for simulating fractional order dynamical control system,” The ANZIAM Journal, vol. 47, pp. C168–C184, 2005.
- K. Diethelm and N. J. Ford, “Multi-order fractional differential equations and their numerical solution,” Applied Mathematics and Computation, vol. 154, no. 3, pp. 621–640, 2004.
- V. Daftardar-Gejji and A. Babakhani, “Analysis of a system of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 293, no. 2, pp. 511–522, 2004.
- M. Unser and T. Blu, “Construction of fractional spline wavelet bases,” in Wavelets Applications in Signal and Image Processing VII, vol. 3813 of Proceedings of SPIE, pp. 422–431, Denver, Colo, USA, July 1999.
- S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, San Diego, Calif, USA, 2nd edition, 1998.
- M. Unser and T. Blu, “Fractional splines and wavelets,” SIAM Review, vol. 42, no. 1, pp. 43–67, 2000.
- M. Unser, A. Aldroubi, and M. Eden, “A family of polynomial spline wavelet transforms,” Signal Processing, vol. 30, pp. 141–162, 1993.
- V. J. Ervin and J. P. Roop, “Variational formulation for the stationary fractional advection dispersion equation,” Numerical Methods for Partial Differential Equations, vol. 22, no. 3, pp. 558–576, 2005.
- F. Mainardi and R. Gorenflo, “On Mittag-Leffler-type functions in fractional evolution processes,” Journal of Computational and Applied Mathematics, vol. 118, no. 1-2, pp. 283–299, 2000.