Copyright © 2012 Jianping Zhao 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. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
2. R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific Publishing, River Edge, NJ, USA, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
3. B. J. West, M. Bologna, and P. Grigolini, Physics of Fractal Operators, Springer, New York, NY, USA, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
4. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993. View at Zentralblatt MATH
5. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science, Yverdon, Switzerland, 1993. View at Zentralblatt MATH
6. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. View at Zentralblatt MATH
7. K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, NY, USA, 1974. View at Zentralblatt MATH
8. V. Kiryakova, Generalized Fractional Calculus and Applications, vol. 301 of Pitman Research Notes in Mathematics Series, Longman Scientific & Technical, Harlow, UK, 1994. View at Zentralblatt MATH
9. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1999. View at Zentralblatt MATH
10. J. Sabatier, O. P. Agrawal, and J. A. T. Machado, Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, New York, NY, USA, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
11. F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, Imperial College Press, London, UK, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
12. D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus: Models and Numerical Methods, vol. 3 of Series on Complexity, Nonlinearity and Chaos, World Scientific Publishing, Boston, Mass, USA, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
13. X. J. Yang, Local Fractional Functional Analysis and Its Applications, Asian Academic Publisher, Hong Kong.
14. X. J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, NY, USA, 2012.
15. A. H. A. Ali, “The modified extended tanh-function method for solving coupled MKdV and coupled Hirota-Satsuma coupled KdV equations,” Physics Letters. A, vol. 363, no. 5-6, pp. 420–425, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
16. C. Li, A. Chen, and J. Ye, “Numerical approaches to fractional calculus and fractional ordinary differential equation,” Journal of Computational Physics, vol. 230, no. 9, pp. 3352–3368, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
17. G. H. Gao, Z. Z. Sun, and Y. N. Zhang, “A finite difference scheme for fractional sub-diffusion equations on an unbounded domain using artificial boundary conditions,” Journal of Computational Physics, vol. 231, no. 7, pp. 2865–2879, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
18. W. Deng, “Finite element method for the space and time fractional Fokker-Planck equation,” SIAM Journal on Numerical Analysis, vol. 47, no. 1, pp. 204–226, 2008/09. View at Publisher · View at Google Scholar
19. S. Momani, Z. Odibat, and V. S. Erturk, “Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation,” Physics Letters. A, vol. 370, no. 5-6, pp. 379–387, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
20. Z. Odibat and S. Momani, “A generalized differential transform method for linear partial differential equations of fractional order,” Applied Mathematics Letters, vol. 21, no. 2, pp. 194–199, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
21. Y. Hu, Y. Luo, and Z. Lu, “Analytical solution of the linear fractional differential equation by Adomian decomposition method,” Journal of Computational and Applied Mathematics, vol. 215, no. 1, pp. 220–229, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
22. 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
23. 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
24. Z. Odibat and S. Momani, “The variational iteration method: an efficient scheme for handling fractional partial differential equations in fluid mechanics,” Computers & Mathematics with Applications, vol. 58, no. 11-12, pp. 2199–2208, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
25. M. Inc, “The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method,” Journal of Mathematical Analysis and Applications, vol. 345, no. 1, pp. 476–484, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
26. 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
27. 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
28. E. Fan, “Soliton solutions for a generalized Hirota-Satsuma coupled KdV equation and a coupled MKdV equation,” Physics Letters. A, vol. 282, no. 1-2, pp. 18–22, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
29. 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
30. 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
31. M. L. Wang, “Solitary wave solutions for variant Boussinesq equations,” Physics Letters. A, vol. 199, no. 3-4, pp. 169–172, 1995. View at Publisher · View at Google Scholar
32. 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
33. G. Jumarie, “Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution,” Journal of Applied Mathematics & Computing, vol. 24, no. 1-2, pp. 31–48, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
34. 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
35. 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
36. G. Jumarie, “Cauchy's integral formula via the modified Riemann-Liouville derivative for analytic functions of fractional order,” Applied Mathematics Letters, vol. 23, no. 12, pp. 1444–1450, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
37. J. H. He, S. K. Elagan, and Z. B. Li, “Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus,” Physics Letters. A, vol. 376, no. 4, pp. 257–259, 2012. View at Publisher · View at Google Scholar
38. J. H. He, “Asymptotic methods for solitary solutions and compacts,” Abstract and applied analysis. In press. View at Publisher · View at Google Scholar
39. S. E. Esipov, “Coupled Burgers equations: a model of polydispersive sedimentation,” Physical Review E, vol. 52, no. 4, pp. 3711–3718, 1995. View at Publisher · View at Google Scholar · View at Scopus
40. A. A. Soliman, “The modified extended tanh-function method for solving Burgers-type equations,” Physica A, vol. 361, no. 2, pp. 394–404, 2006. View at Publisher · View at Google Scholar