- 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
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 819268, 9 pages
Variational Approximate Solutions of Fractional Nonlinear Nonhomogeneous Equations with Laplace Transform
1School of Mathematical Sciences, Dezhou University, Dezhou 253023, China
2The Center of Data Processing and Analyzing, Dezhou University, Dezhou 253023, China
Received 11 May 2013; Accepted 14 August 2013
Academic Editor: Rodrigo Lopez Pouso
Copyright © 2013 Yanqin Liu 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.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific Publishing, River Edge, NJ, USA, 2000.
- R. Metzler and J. Klafter, “The random walk's guide to anomalous diffusion: a fractional dynamics approach,” Physics Reports, vol. 339, no. 1, p. 77, 2000.
- K. Diethelm and N. J. Ford, “Multi-order fractional differential equations and their numerical solution,” Applied Mathematics and Computation, vol. 154, no. 3, pp. 621–640, 2004.
- F. W. Liu, V. Anh, and I. Turner, “Numerical solution of the space fractional Fokker-Planck equation,” Journal of Computational and Applied Mathematics, vol. 166, no. 1, pp. 209–219, 2004.
- 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, Boston, Mass, USA, 2012.
- J. S. Duan, R. Rach, D. Buleanu, and A. M. Wazwaz, “A review of the Adomian decomposition method and its applicaitons to fractional differential equations,” Communications in Fractional Calculus, vol. 3, pp. 73–99, 2012.
- J.-H. He, “Variational iteration method—a kind of non-linear analytical technique: some examples,” International Journal of Non-Linear Mechanics, vol. 34, no. 4, pp. 699–708, 1999.
- A.-M. Wazwaz, “The variational iteration method for analytic treatment of linear and nonlinear ODEs,” Applied Mathematics and Computation, vol. 212, no. 1, pp. 120–134, 2009.
- V. S. Erturk, S. Momani, and Z. Odibat, “Application of generalized differential transform method to multi-order fractional differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 8, pp. 1642–1654, 2008.
- J.-H. He, “Homotopy perturbation method: a new nonlinear analytical technique,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 73–79, 2003.
- 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.
- X. Y. Jiang and H. T. Qi, “Thermal wave model of bioheat transfer with modified Riemann-Liouville fractional derivative,” Journal of Physics, vol. 45, no. 48, Article ID 485101, 2012.
- J. H. Ma and Y. Q. Liu, “Exact solutions for a generalized nonlinear fractional Fokker-Planck equation,” Nonlinear Analysis. Real World Applications, vol. 11, no. 1, pp. 515–521, 2010.
- Y.-Q. Liu and J.-H. Ma, “Exact solutions of a generalized multi-fractional nonlinear diffusion equation in radical symmetry,” Communications in Theoretical Physics, vol. 52, no. 5, pp. 857–861, 2009.
- Y. Q. Liu, “Approximate solutions of fractional nonlinear equations using homotopy perturbation transformation method,” Abstract and Applied Analysis, vol. 2012, Article ID 752869, 14 pages, 2012.
- Y. Q. Liu, “Study on space-time fractional nonlinear biological equation in radial symmetry,” Mathematical Problems in Engineering, vol. 2013, Article ID 654759, 6 pages, 2013.
- Y. Q. Liu, “Variational homotopy perturbation method for solving fractional initial boundary value problems,” Abstract and Applied Analysis, vol. 2012, Article ID 727031, 10 pages, 2012.
- S. M. Guo, L. Q. Mei, and Y. Li, “Fractional variational homotopy perturbation iteration method and its application to a fractional diffusion equation,” Applied Mathematics and Computation, vol. 219, no. 11, pp. 5909–5917, 2013.
- J.-H. He, “Variational iteration method—some recent results and new interpretations,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 3–17, 2007.
- G.-C. Wu and D. Baleanu, “Variational iteration method for fractional calculus—a universal approach by Laplace transform,” Advances in Difference Equations, vol. 2013, article 18, 9 pages, 2013.
- G. C. Wu, “Laplace tranform overcoming principle drawbacks in applicaiton of the variation iteration method to fractional heat equations,” Thermal Science, vol. 16, no. 4, pp. 1257–1261, 2012.
- A. Ghorbani, “Beyond Adomian polynomials: He polynomials,” Chaos, Solitons and Fractals, vol. 39, no. 3, pp. 1486–1492, 2009.
- H. Jafari, M. Alipour, and H. Tajadodi, “Two-dimensional differential transform method for solving nonlinear partial differential equaitons,” International Journal of Research and Reviews in Applied Sciences, vol. 2, no. 1, pp. 47–52, 2010.
- S. Momani and Z. Odibat, “A novel method for nonlinear fractional partial differential equations: combination of DTM and generalized Taylor's formula,” Journal of Computational and Applied Mathematics, vol. 220, no. 1-2, pp. 85–95, 2008.
- N. H. Sweilam and M. M. Khader, “Variational iteration method for one dimensional nonlinear thermoelasticity,” Chaos, Solitons & Fractals, vol. 32, no. 1, pp. 145–149, 2007.