- About this Journal
- Abstracting and Indexing
- 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 2012 (2012), Article ID 472030, 14 pages
Solving the Fractional Rosenau-Hyman Equation via Variational Iteration Method and Homotopy Perturbation Method
1Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Medan UNIMED 20221, Medan, Sumatera Utara, Indonesia
2School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia UKM, 43600 Bangi, Selangor, Malaysia
Received 31 May 2012; Accepted 8 November 2012
Academic Editor: Shaher Momani
Copyright © 2012 R. Yulita Molliq and M. S. M. Noorani. 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.
- J. H. He, “Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics,” International Journal of Turbo and Jet Engines, vol. 14, no. 1, pp. 23–28, 1997.
- J. H. He, “Some applications of nonlinear fractional differential equations and their approximations,” Bulletin of Science, Technology & Society, vol. 15, no. 2, pp. 86–90, 1999.
- J. H. He, “Approximate analytical solution for seepage flow with fractional derivatives in porous media,” Computer Methods in Applied Mechanics and Engineering, vol. 167, no. 1-2, pp. 57–68, 1998.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- K. Al-Khaled and S. Momani, “An approximate solution for a fractional diffusion-wave equation using the decomposition method,” Applied Mathematics and Computation, vol. 165, no. 2, pp. 473–483, 2005.
- F. Mainardi, Y. Luchko, and G. Pagnini, “The fundamental solution of the space-time fractional diffusion equation,” Fractional Calculus & Applied Analysis, vol. 4, no. 2, pp. 153–192, 2001.
- A. Hanyga, “Multidimensional solutions of time-fractional diffusion-wave equations,” Proceedings of the Royal Society of London, Series A, vol. 458, no. 2020, pp. 933–957, 2002.
- F. Huang and F. Liu, “The time fractional diffusion equation and the advection-dispersion equation,” The Australian & New Zealand Industrial and Applied Mathematics Journal, vol. 46, no. 3, pp. 317–330, 2005.
- F. Huang and F. Liu, “The fundamental solution of the space-time fractional advection-dispersion equation,” Journal of Applied Mathematics & Computing, vol. 18, no. 1-2, pp. 339–350, 2005.
- S. Momani, “An explicit and numerical solutions of the fractional KdV equation,” Mathematics and Computers in Simulation, vol. 70, no. 2, pp. 110–118, 2005.
- L. Debnath and D. D. Bhatta, “Solutions to few linear fractional inhomogeneous partial differential equations in fluid mechanics,” Fractional Calculus & Applied Analysis, vol. 7, no. 1, pp. 21–36, 2004.
- J. H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257–262, 1999.
- 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.
- J. H. He, “Periodic solutions and bifurcations of delay-differential equations,” Physics Letters A, vol. 347, no. 4–6, pp. 228–230, 2005.
- J. H. He, “Application of homotopy perturbation method to nonlinear wave equations,” Chaos, Solitons and Fractals, vol. 26, no. 3, pp. 695–700, 2005.
- J. H. He, “Limit cycle and bifurcation of nonlinear problems,” Chaos, Solitons and Fractals, vol. 26, no. 3, pp. 827–833, 2005.
- J. H. He, Non-perturbative methods for strongly nonlinear problems [Dissertation], de-Verlag im Internet GmbH, Berlin, Germany, 2006.
- J. H. 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 delay differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 2, no. 4, pp. 235–236, 1997.
- M. Tatari and M. Dehghan, “On the convergence of He's variational iteration method,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 121–128, 2007.
- Z. Odibat and S. Momani, “Numerical methods for nonlinear partial differential equations of fractional order,” Applied Mathematical Modelling, vol. 32, no. 1, pp. 28–39, 2008.
- R. Yulita Molliq, M. S. M. Noorani, and I. Hashim, “Variational iteration method for fractional heat- and wave-like equations,” Nonlinear Analysis: Real World Applications, vol. 10, no. 3, pp. 1854–1869, 2009.
- R. Yulita Molliq, M. S. M. Noorani, I. Hashim, and R. R. Ahmad, “Approximate solutions of fractional Zakharov-Kuznetsov equations by VIM,” Journal of Computational and Applied Mathematics, vol. 233, no. 2, pp. 103–108, 2009.
- C. Chun, “Variational iteration method for a reliable treatment of heat equations with ill-defined initial data,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 9, no. 4, pp. 435–440, 2008.
- M. G. Porshokouhi and B. Ghanbari, “Application of He's variational iteration method for solution of the family of Kuramoto-Sivashinsky equations,” Journal of King Saud University - Science, vol. 23, no. 4, pp. 407–411, 2011.
- S. T. Mohyud-Din and A. Yildirim, “An algorithm for solving the fractional vibration equation,” Computational Mathematics and Modeling, vol. 23, no. 2, pp. 228–237, 2012.
- A. M. A. El-Sayed, A. Elsaid, I. L. El-Kalla, and D. Hammad, “A homotopy perturbation technique for solving partial differential equations of fractional order in finite domains,” Applied Mathematics and Computation, vol. 218, no. 17, pp. 8329–8340, 2012.
- P. Rosenau and J. M. Hyman, “Compactons: solitons with finite wavelength,” Physical Review Letters, vol. 70, no. 5, pp. 564–567, 1993.
- R. Gorenflo and F. Mainardi, “Fractional calculus: integral and differential equations of fractional order,” in Fractals and Fractional Calculus, A. Carpinteri and F. Mainardi, Eds., Springer, New York, NY, USA, 1997.
- M. Caputo, “Linear models of dissipation whose Q is almost frequency independent II,” Geophysical Journal of the Royal Astronomical Society, vol. 13, no. 5, pp. 529–539, 1967.
- M. Inokuti, H. Sekine, and T. Mura, “General use of the Lagrange multiplier in nonlinear mathematical physics,” in Variational Method in the Mechanics of Solids, S. Nemat Nasser, Ed., pp. 156–162, Pergamon Press, New York, NY, USA, 1978.
- B. A. Finlayson, The Method of Weighted Residuals and Variational Principles, Academic Press, New York, NY, USA, 1972.
- P. A. Clarkson, E. L. Mansfield, and T. J. Priestley, “Symmetries of a class of nonlinear third-order partial differential equations,” Mathematical and Computer Modelling, vol. 25, no. 8-9, pp. 195–212, 1997.