About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 282190, 10 pages
http://dx.doi.org/10.1155/2014/282190
Research Article

Numerical Treatment of the Modified Time Fractional Fokker-Planck Equation

School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China

Received 26 December 2013; Revised 8 February 2014; Accepted 16 February 2014; Published 27 March 2014

Academic Editor: Adem Kilicman

Copyright © 2014 Yuxin Zhang. 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. S. Miller and B. Ross, An Introduction To the Fractional Calculus and Fractional Differential Equations, John Wiley, New York, NY, USA, 1993.
  2. I. Podlubny, Fractional Differential Equations, Academic Press, 1999.
  3. A. Barari, M. Omidvar, A. R. Ghotbi, and D. D. Ganji, “Application of homotopy perturbation method and variational iteration method to nonlinear oscillator differential equations,” Acta Applicandae Mathematicae, vol. 104, no. 2, pp. 161–171, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. S. Das, “Analytical solution of a fractional diffusion equation by variational iteration method,” Computers and Mathematics with Applications, vol. 57, no. 3, pp. 483–487, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. D. D. Ganji and A. Sadighi, “Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 24–34, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  6. E. Hesameddini and F. Fotros, “Solution for time-fractional coupled Klein-Gordon Schrodinger equation using decomposition method,” International Mathematics Olympiad, vol. 7, pp. 1047–1056, 2012. View at Zentralblatt MATH
  7. G.-C. Wu and E. W. M. Lee, “Fractional variational iteration method and its application,” Physics Letters A, vol. 374, no. 25, pp. 2506–2509, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. C.-M. Chen, F. Liu, and K. Burrage, “Finite difference methods and a fourier analysis for the fractional reaction-subdiffusion equation,” Applied Mathematics and Computation, vol. 198, no. 2, pp. 754–769, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. C. Çelik and M. Duman, “Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative,” Journal of Computational Physics, vol. 231, no. 4, pp. 1743–1750, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. X. Hu and L. Zhang, “Implicit compact difference schemes for the fractional cable equation,” Applied Mathematical Modelling, vol. 36, pp. 4027–4043, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. M. M. Meerschaert and C. Tadjeran, “Finite difference approximations for two-sided space-fractional partial differential equations,” Applied Numerical Mathematics, vol. 56, no. 1, pp. 80–90, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. D. K. Salkuyeh, “On the finite difference approximation to the convection-diffusion equation,” Applied Mathematics and Computation, vol. 179, no. 1, pp. 79–86, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. E. Sousa, “Numerical approximations for fractional diffusion equations via splines,” Computers and Mathematics with Applications, vol. 62, no. 3, pp. 938–944, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. E. Sousa, “Finite difference approximations for a fractional advection diffusion problem,” Journal of Computational Physics, vol. 228, no. 11, pp. 4038–4054, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. C. Tadjeran and M. M. Meerschaert, “A second-order accurate numerical method for the two-dimensional fractional diffusion equation,” Journal of Computational Physics, vol. 220, no. 2, pp. 813–823, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  16. S. B. Yuste and L. Acedo, “An explicit finite difference method and a new von Neumann-type stability analysis for fractional diffusion equations,” SIAM Journal on Numerical Analysis, vol. 42, no. 5, pp. 1862–1874, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. Q. Yang, F. Liu, and I. Turner, “Numerical methods for fractional partial differential equations with Riesz space fractional derivatives,” Applied Mathematical Modelling, vol. 34, no. 1, pp. 200–218, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  18. B. I. Henry, T. A. M. Langlands, and P. Straka, “Fractional Fokker-Planck equations for subdiffusion with space- and time-dependent forces,” Physical Review Letters, vol. 105, no. 17, Article ID 170602, 2010. View at Publisher · View at Google Scholar · View at Scopus