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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 398286, 8 pages
http://dx.doi.org/10.1155/2014/398286
Research Article

Numerical Methods for Fractional Order Singular Partial Differential Equations with Variable Coefficients

1Faculty of Science and Technology, Universiti Sains Islam Malaysia, 71800 Nilai, Malaysia
2Department of Mathematics, Zawia University, Zawia, Libya
3Department of Mathematics and Institute of Mathematical Research, University Putra Malaysia, 4300 Serdang, Selangor, Malaysia

Received 11 October 2013; Accepted 22 January 2014; Published 10 March 2014

Academic Editor: Abdon Atangana

Copyright © 2014 Asma Ali Elbeleze et al. 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. Diethelm and A. D. Freed, “On the solution of nonlinear fractional order differential equations used in the modeling of viscoelasticity,” in Scientific Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties, F. Keil, W. Mackens, H. Voss, and J. Werther, Eds., pp. 217–224, Springer, Heidelberg, Germany, 1999. View at Google Scholar
  2. R. Metzler, W. Schick, H. G. Kilian, and T. F. Nonnenmacher, “Relaxation in filled polymers: a fractional calculus approach,” The Journal of Chemical Physics, vol. 103, no. 16, pp. 7180–7186, 1995. View at Publisher · View at Google Scholar · View at Scopus
  3. R. Hilfer, Applications of Fractional Calculus in Physics, World scientific, Singapore, 2000.
  4. K. B. Oldham and J. Spanier, “The fractional calculus,” in Mathematics in Science and Engineering, vol. 198, Academic Press, San Diego, Calif, USA, 1974. View at Google Scholar
  5. I. Podlubny, “Fractional differential equation,” in Mathematics in Science and Engineering, vol. 198, Academic Press, San Diego, Calif, USA, 1999. View at Google Scholar
  6. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993.
  7. S. T. Mohydud-Din, A. Yildirim, M. M. Hosseini, and Y. Khan, “A study on systems of variable-coefficient singular parabolic partial differential equations,” World Applied Sciences Journal, vol. 10, no. 11, pp. 1321–1327, 2010. View at Google Scholar
  8. M. Abokhald, “Varational iteration method for nonlinear singular two-point boundary value problems arising in human physiology,” Journal of Mathematics, vol. 2013, Article ID 720134, 4 pages, 2013. View at Publisher · View at Google Scholar
  9. S. Abbasbsndy and E. Shivanian, “Solution of singular linear vibrational BVPs by the homotopy analysis method,” Journal of Numerical Mathematics and Stochastics, vol. 1, no. 1, pp. 77–84, 2009. View at Google Scholar
  10. J. H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257–262, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. J. H. He, “Coupling method of a homotopy technique and a perturbation technique for non-linear problems,” International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37–43, 2000. View at Publisher · View at Google Scholar · View at Scopus
  12. J. H. He, Non-pertubation methods for strongly nonlinear problems [Dissertation], de-Verlag im Internet Gmbh, Berlin, Germany, 2006.
  13. J. H. He, “Variational iteration method for delay differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 2, no. 4, pp. 235–236, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. J. H. He, “Approximate solution of non linear differential equations with convolution product nonlinearities,” Computer Methods in Applied Mechanics and Engineering, vol. 167, pp. 69–73, 1998. View at Google Scholar
  15. J. H. He, “Approximate analytical solution for seepage flow with fractional derivatives in porous media,” Computer Methods in Applied Mechanics and Engineering, vol. 167, no. 1-2, pp. 57–68, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  16. J. H. He, “Variational iteration method—a kind of non-linear analytical technique: some examples,” International Journal of Non-Linear Mechanics, vol. 34, no. 4, pp. 699–708, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. M. Inokuti, H. Sekine, and T. Mura, “General use of the Lagrange multiplier in non-linear mathematical physics,” in Variational Method in the Mechanics of Solids, S. Nemat-Nasser, Ed., pp. 156–162, Pergamon Press, Oxford, UK, 1978. View at Google Scholar