About this Journal Submit a Manuscript Table of Contents
International Journal of Differential Equations
Volume 2010 (2010), Article ID 764738, 8 pages
http://dx.doi.org/10.1155/2010/764738
Research Article

He's Variational Iteration Method for Solving Fractional Riccati Differential Equation

Department of Mathematics and Computer Science, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran

Received 10 August 2009; Accepted 28 January 2010

Academic Editor: Shaher M. Momani

Copyright © 2010 H. Jafari and H. Tajadodi. 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. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. View at MathSciNet
  2. K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, NY, USA, 1974. View at MathSciNet
  3. H. Jafari and V. Daftardar-Gejji, “Solving a system of nonlinear fractional differential equations using Adomian decomposition,” Journal of Computational and Applied Mathematics, vol. 196, no. 2, pp. 644–651, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. G. Lu and G. Chen, “A note on the fractional-order Chen system,” Chaos, Solitons & Fractals, vol. 27, no. 3, pp. 685–688, 2006. View at Publisher · View at Google Scholar
  5. 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 Zentralblatt MATH
  6. J.-H. He, “Variational iteration method for autonomous ordinary differential systems,” Applied Mathematics and Computation, vol. 114, no. 2-3, pp. 115–123, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J.-H. He, “Variational principles for some nonlinear partial differential equations with variable coefficients,” Chaos, Solitons & Fractals, vol. 19, no. 4, pp. 847–851, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. A. Abdou and A. A. Soliman, “New applications of variational iteration method,” Physica D, vol. 211, no. 1-2, pp. 1–8, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Momani and S. Abuasad, “Application of He's variational iteration method to Helmholtz equation,” Chaos, Solitons & Fractals, vol. 27, no. 5, pp. 1119–1123, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Z. M. Odibat and S. Momani, “Application of variational iteration method to nonlinear differential equations of fractional order,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 1, pp. 27–34, 2006.
  11. S. Momani and Z. Odibat, “Numerical approach to differential equations of fractional order,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 96–110, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J.-H. He, “Some asymptotic methods for strongly nonlinear equations,” International Journal of Modern Physics B, vol. 20, no. 10, pp. 1141–1199, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. H. Jafari, H. Hosseinzadeh, and E. Salehpoor, “A new approach to the gas dynamics equation: an application of the variational iteration method,” Applied Mathematical Sciences, vol. 2, no. 48, pp. 2397–2400, 2008. View at Zentralblatt MATH · View at MathSciNet
  14. H. Jafari, A. Golbabai, E. Salehpoor, and Kh. Sayehvand, “Application of variational iteration method for Stefan problem,” Applied Mathematical Sciences, vol. 2, no. 60, pp. 3001–3004, 2008. View at MathSciNet
  15. H. Jafari and A. Alipoor, “A new method for calculating General Lagrange's multiplier in the variational iteration method,” Numerical Method for Partial Differential Equations, In press, 2010.
  16. J. Cang, Y. Tan, H. Xu, and S.-J. Liao, “Series solutions of non-linear Riccati differential equations with fractional order,” Chaos, Solitons & Fractals, vol. 40, no. 1, pp. 1–9, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  17. S. Momani and N. Shawagfeh, “Decomposition method for solving fractional Riccati differential equations,” Applied Mathematics and Computation, vol. 182, no. 2, pp. 1083–1092, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. Z. Odibat and S. Momani, “Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order,” Chaos, Solitons & Fractals, vol. 36, no. 1, pp. 167–174, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet