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International Journal of Differential Equations
Volume 2010 (2010), Article ID 764738, 8 pages
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.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, NY, USA, 1974.
- 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.
- 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.
- 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.
- J.-H. He, “Variational iteration method for autonomous ordinary differential systems,” Applied Mathematics and Computation, vol. 114, no. 2-3, pp. 115–123, 2000.
- 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.
- M. A. Abdou and A. A. Soliman, “New applications of variational iteration method,” Physica D, vol. 211, no. 1-2, pp. 1–8, 2005.
- 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.
- 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.
- 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.
- J.-H. He, “Some asymptotic methods for strongly nonlinear equations,” International Journal of Modern Physics B, vol. 20, no. 10, pp. 1141–1199, 2006.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.