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Mathematical Problems in Engineering
Volume 2011, Article ID 341989, 11 pages
http://dx.doi.org/10.1155/2011/341989
Research Article

Numerical Solution of Nonlinear Fredholm Integrodifferential Equations of Fractional Order by Using Hybrid of Block-Pulse Functions and Chebyshev Polynomials

Department of Science, Huaihai Institute of Technology, Lianyungang, Jiangsu 222005, China

Received 2 June 2011; Accepted 23 August 2011

Academic Editor: Rafael Martinez-Guerra

Copyright © 2011 Changqing Yang. 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. J. H. He, “Some applications of nonlinear fractional differential equations and their approximations,” Bulletin of Science, Technology, vol. 15, no. 2, pp. 86–90, 1999. View at Google Scholar
  2. J. A. T. Machado, “Analysis and design of fractional-order digital control systems,” Systems Analysis Modelling Simulation, vol. 27, no. 2-3, pp. 107–122, 1997. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  3. I. Hashim, O. Abdulaziz, and S. Momani, “Homotopy analysis method for fractional IVPs,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 3, pp. 674–684, 2009. View at Publisher · View at Google Scholar
  4. Ü. Lepik, “Solving fractional integral equations by the Haar wavelet method,” Applied Mathematics and Computation, vol. 214, no. 2, pp. 468–478, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. 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
  6. S. Momani and N. Shawagfeh, “Decomposition method for solving fractional Riccati differential equations,” Applied Mathematics and Computation, vol. 182, no. 2, pp. 1083–1092, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. S. Momani and M. A. Noor, “Numerical methods for fourth-order fractional integro-differential equations,” Applied Mathematics and Computation, vol. 182, no. 1, pp. 754–760, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. V. Daftardar-Gejji and H. Jafari, “Solving a multi-order fractional differential equation using Adomian decomposition,” Applied Mathematics and Computation, vol. 189, no. 1, pp. 541–548, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. S. S. Ray, K. S. Chaudhuri, and R. K. Bera, “Analytical approximate solution of nonlinear dynamic system containing fractional derivative by modified decomposition method,” Applied Mathematics and Computation, vol. 182, no. 1, pp. 544–552, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. Q. Wang, “Numerical solutions for fractional KdV-Burgers equation by Adomian decomposition method,” Applied Mathematics and Computation, vol. 182, no. 2, pp. 1048–1055, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. J.-F. Cheng and Y.-M. Chu, “Solution to the linear fractional differential equation using Adomian decomposition method,” Mathematical Problems in Engineering, vol. 2011, Article ID 587068, 14 pages, 2011. View at Google Scholar · View at Zentralblatt MATH
  12. M. Inc, “The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method,” Journal of Mathematical Analysis and Applications, vol. 345, no. 1, pp. 476–484, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. S. Momani and Z. Odibat, “Analytical approach to linear fractional partial differential equations arising in fluid mechanics,” Physics Letters A, vol. 355, no. 4-5, pp. 271–279, 2006. View at Publisher · View at Google Scholar · View at Scopus
  14. F. Dal, “Application of variational iteration method to fractional hyperbolic partial differential equations,” Mathematical Problems in Engineering, vol. 2009, Article ID 824385, 10 pages, 2009. View at Google Scholar · View at Zentralblatt MATH
  15. S. Momani and Z. Odibat, “Homotopy perturbation method for nonlinear partial differential equations of fractional order,” Physics Letters A, vol. 365, no. 5-6, pp. 345–350, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. N. H. Sweilam, M. M. Khader, and R. F. Al-Bar, “Numerical studies for a multi-order fractional differential equation,” Physics Letters A, vol. 371, no. 1-2, pp. 26–33, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. E. A. Rawashdeh, “Numerical solution of fractional integro-differential equations by collocation method,” Applied Mathematics and Computation, vol. 176, no. 1, pp. 1–6, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. 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, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. P. Kumar and O. P. Agrawal, “An approximate method for numerical solution of fractional differential equations,” Signal Processing, vol. 86, no. 10, pp. 2602–2610, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  20. F. Liu, V. Anh, and I. Turner, “Numerical solution of the space fractional Fokker-Planck equation,” Journal of Computational and Applied Mathematics, vol. 166, no. 1, pp. 209–219, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  21. S. B. Yuste, “Weighted average finite difference methods for fractional diffusion equations,” Journal of Computational Physics, vol. 216, no. 1, pp. 264–274, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Equations, to Methods of Their Solution and Some of Their Applications, vol. 198 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1999.
  23. M. Razzaghi and H.-R. Marzban, “Direct method for variational problems via hybrid of block-pulse and Chebyshev functions,” Mathematical Problems in Engineering, vol. 6, no. 1, pp. 85–97, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. A. Kilicman and Z. A. A. Al Zhour, “Kronecker operational matrices for fractional calculus and some applications,” Applied Mathematics and Computation, vol. 187, no. 1, pp. 250–265, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. M. T. Kajani and A. H. Vencheh, “Solving second kind integral equations with hybrid Chebyshev and block-pulse functions,” Applied Mathematics and Computation, vol. 163, no. 1, pp. 71–77, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. H. Saeedi, M. M. Moghadam, N. Mollahasani, and G. N. Chuev, “A CAS wavelet method for solving nonlinear Fredholm Integro-differential equations of fractional order,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1154–1163, 2011. View at Publisher · View at Google Scholar