- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 282190, 10 pages
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.
- K. S. Miller and B. Ross, An Introduction To the Fractional Calculus and Fractional Differential Equations, John Wiley, New York, NY, USA, 1993.
- I. Podlubny, Fractional Differential Equations, Academic Press, 1999.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- X. Hu and L. Zhang, “Implicit compact difference schemes for the fractional cable equation,” Applied Mathematical Modelling, vol. 36, pp. 4027–4043, 2012.
- 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.
- 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.
- E. Sousa, “Numerical approximations for fractional diffusion equations via splines,” Computers and Mathematics with Applications, vol. 62, no. 3, pp. 938–944, 2011.
- E. Sousa, “Finite difference approximations for a fractional advection diffusion problem,” Journal of Computational Physics, vol. 228, no. 11, pp. 4038–4054, 2009.
- 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.
- 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.
- 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.
- 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.