Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 256823, 5 pages
http://dx.doi.org/10.1155/2013/256823
Research Article

A New Approach for Solving Fractional Partial Differential Equations

School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Received 20 January 2013; Accepted 18 April 2013

Academic Editor: Livija Cveticanin

Copyright © 2013 Fanwei Meng. 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. A. Saadatmandi and M. Dehghan, “A new operational matrix for solving fractional-order differential equations,” Computers & Mathematics with Applications, vol. 59, no. 3, pp. 1326–1336, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. Y. Zhou, F. Jiao, and J. Li, “Existence and uniqueness for p-type fractional neutral differential equations,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 71, no. 7-8, pp. 2724–2733, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  3. L. Galeone and R. Garrappa, “Explicit methods for fractional differential equations and their stability properties,” Journal of Computational and Applied Mathematics, vol. 228, no. 2, pp. 548–560, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. C. Trigeassou, N. Maamri, J. Sabatier, and A. Oustaloup, “A Lyapunov approach to the stability of fractional differential equations,” Signal Processing, vol. 91, no. 3, pp. 437–445, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. W. Deng, “Smoothness and stability of the solutions for nonlinear fractional differential equations,” Nonlinear Analysis: Theory, Methods & Applications A, vol. 72, no. 3-4, pp. 1768–1777, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. F. Ghoreishi and S. Yazdani, “An extension of the spectral Tau method for numerical solution of multi-order fractional differential equations with convergence analysis,” Computers & Mathematics with Applications, vol. 61, no. 1, pp. 30–43, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. T. Edwards, N. J. Ford, and A. C. Simpson, “The numerical solution of linear multi-term fractional differential equations: systems of equations,” Journal of Computational and Applied Mathematics, vol. 148, no. 2, pp. 401–418, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. Muslim, “Existence and approximation of solutions to fractional differential equations,” Mathematical and Computer Modelling, vol. 49, no. 5-6, pp. 1164–1172, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. M. A. El-Sayed and M. Gaber, “The Adomian decomposition method for solving partial differential equations of fractal order in finite domains,” Physics Letters A, vol. 359, no. 3, pp. 175–182, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. A. M. A. El-Sayed, S. H. Behiry, and W. E. Raslan, “Adomian's decomposition method for solving an intermediate fractional advection-dispersion equation,” Computers & Mathematics with Applications, vol. 59, no. 5, pp. 1759–1765, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. He, “A new approach to nonlinear partial differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 2, no. 4, pp. 230–235, 1997. View at Publisher · View at Google Scholar · View at Scopus
  12. 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 MathSciNet
  13. S. Guo and L. Mei, “The fractional variational iteration method using He's polynomials,” Physics Letters A, vol. 375, no. 3, pp. 309–313, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. 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 MathSciNet
  15. J.-H. He, “A 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 MathSciNet
  16. Z. Odibat and S. Momani, “A generalized differential transform method for linear partial differential equations of fractional order,” Applied Mathematics Letters of Rapid Publication, vol. 21, no. 2, pp. 194–199, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. M. Cui, “Compact finite difference method for the fractional diffusion equation,” Journal of Computational Physics, vol. 228, no. 20, pp. 7792–7804, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. Q. Huang, G. Huang, and H. Zhan, “A finite element solution for the fractional advection-dispersion equation,” Advances in Water Resources, vol. 31, no. 12, pp. 1578–1589, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. S. Guo, L. Mei, Y. Li, and Y. Sun, “The improved fractional sub-equation method and its applications to the space-time fractional differential equations in fluid mechanics,” Physics Letters A, vol. 376, no. 4, pp. 407–411, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. B. Lu, “Bäcklund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations,” Physics Letters A, vol. 376, no. 28-29, pp. 2045–2048, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  21. S. Zhang and H.-Q. Zhang, “Fractional sub-equation method and its applications to nonlinear fractional PDEs,” Physics Letters A, vol. 375, no. 7, pp. 1069–1073, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. G. Jumarie, “Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results,” Computers & Mathematics with Applications, vol. 51, no. 9-10, pp. 1367–1376, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet