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International Journal of Differential Equations
Volume 2010 (2010), Article ID 464321, 22 pages
Research Article

Stability and Convergence of an Effective Numerical Method for the Time-Space Fractional Fokker-Planck Equation with a Nonlinear Source Term

School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia

Received 25 May 2009; Revised 20 August 2009; Accepted 28 September 2009

Academic Editor: Om Agrawal

Copyright © 2010 Qianqian Yang 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.

Citations to this Article [9 citations]

The following is the list of published articles that have cited the current article.

  • Svatoslav Stanek, “The existence of positive solutions of singular fractional boundary value problems,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1379–1388, 2011. View at Publisher · View at Google Scholar
  • Changpin Li, and Fanhai Zeng, “Finite Difference Methods For Fractional Differential Equations,” International Journal of Bifurcation and Chaos, vol. 22, no. 4, 2012. View at Publisher · View at Google Scholar
  • F. Zeng, C. Li, and F. Liu, “High-order explicit-implicit numerical methods for nonlinear anomalous diffusion equations,” European Physical Journal-Special Topics, vol. 222, no. 8, pp. 1885–1900, 2013. View at Publisher · View at Google Scholar
  • J. Song, Q. Yu, F. Liu, and I. Turner, “A spatially second-order accurate implicit numerical method for the space and time fractional Bloch-Torrey equation,” Numerical Algorithms, 2013. View at Publisher · View at Google Scholar
  • A. Dzielinski, and P. M. Czyronis, “Fixed final time and free final state optimal control problem for fractional dynamic systems - linear quadratic discrete-time case,” Bulletin of The Polish Academy of Sciences-Technical Sciences, vol. 61, no. 3, pp. 681–690, 2013. View at Publisher · View at Google Scholar
  • Yuxin Zhang, “[3,3] Pade approximation method for solving space fractional Fokker-Planck equations,” Applied Mathematics Letters, vol. 35, pp. 109–114, 2014. View at Publisher · View at Google Scholar
  • Zhengang Zhao, Yunying Zheng, and Peng Guo, “A Galerkin Finite Element Method for a Class of Time–Space Fractional Differential Equation with Nonsmooth Data,” Journal of Scientific Computing, 2015. View at Publisher · View at Google Scholar
  • Ravi Shanker Dubey, Badr Saad T. Alkahtani, and Abdon Atangana, “Analytical Solution of Space-Time Fractional Fokker-Planck Equation by Homotopy Perturbation Sumudu Transform Method,” Mathematical Problems in Engineering, vol. 2015, pp. 1–7, 2015. View at Publisher · View at Google Scholar
  • Lidia Aceto, Cecilia Magherini, and Paolo Novati, “ON THE CONSTRUCTION AND PROPERTIES OF m-STEP METHODS FOR FDEs,” Siam Journal On Scientific Computing, vol. 37, no. 2, pp. A653–A675, 2015. View at Publisher · View at Google Scholar