- 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
International Journal of Differential Equations
Volume 2011 (2011), Article ID 545607, 15 pages
Solving Famous Nonlinear Coupled Equations with Parameters Derivative by Homotopy Analysis Method
Department of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91779-48974, Iran
Received 15 May 2011; Accepted 4 July 2011
Academic Editor: Shaher M. Momani
Copyright © 2011 Sohrab Effati 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.
- M. Caputo, “Linear models of dissipation whose Q is almost frequency independent, part II,” Geophysical Journal of the Royal Astronomical Society, vol. 13, no. 5, pp. 529–539, 1967.
- K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, NY, USA, 1974.
- 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 and Fractals, vol. 36, no. 1, pp. 167–174, 2008.
- Z. Odibat and S. Momani, “Application of variation iteration method to nonlinear differential equations of fractional order,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 1, no. 7, pp. 15–27, 2006.
- S. J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. thesis, Shanghai Jiao Tong University, 1992.
- S. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, CRC Series: Modern Mechanics and Mathematics, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2003.
- S. Liao, “On the homotopy anaylsis method for nonlinear problems,” Applied Mathematics and Computation, vol. 147, pp. 499–513, 2004.
- S. Liao, “Comparison between the homotopy analysis method and homotopy perturbation method,” Applied Mathematics and Computation, vol. 169, no. 2, pp. 1186–1194, 2005.
- S. Liao, “Homotopy analysis method: a new analytical technique for nonlinear problems,” Journal of Communications in Nonlinear Science and Numerical Simulation, vol. 2, no. 2, pp. 95–100, 1997.
- T. Hayat, M. Khan, and M. Ayub, “On non-linear flows with slip boundary condition,” Zeitschrift für Angewandte Mathematik und Physik, vol. 56, no. 6, pp. 1012–1029, 2005.
- S. Abbasbandy and F. S. Zakaria, “Soliton solutions for the 5th-order KdV equation with the homotopy analysis method,” Nonlinear Dynamics, vol. 51, no. 1-2, pp. 83–87, 2008.
- S. P. Zhu, “An exact and explicit solution for the valuation of American put options,” Quantitative Finance, vol. 6, no. 3, pp. 229–242, 2006.
- A. K. Alomari, M. S. M. Noorani, R. Nazar, and C. P. Li, “Homotopy analysis method for solving fractional Lorenz system,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 7, pp. 1864–1872, 2010.
- A. K. Alomari, M. S. M. Noorani, and R. Nazar, “Solution of delay differential equation by means of homotopy analysis method,” Acta Applicandae Mathematicae, vol. 108, no. 2, pp. 395–412, 2009.
- B. J. West, M. Bologna, and P. Grigolini, Physics of Fractal Operators, Institute for Nonlinear Science, Springer, New York, NY, USA, 2003.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication, John Wiley & Sons, New York, NY, USA, 1993.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science Publishers, Yverdon, Switzerland, 1993.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- J. H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257–262, 1999.
- Y. Chen and H. An, “Homotopy perturbation method for a type of nonlinear coupled equations with parameters derivative,” Applied Mathematics and Computation, vol. 204, no. 2, pp. 764–772, 2008.
- E. G. 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.