- 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
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 901540, 13 pages
Generalized Kudryashov Method for Time-Fractional Differential Equations
1Department of Mathematics, Firat University, 23119 Elazig, Turkey
2Department of Mathematics, Bozok University, 66100 Yozgat, Turkey
Received 25 March 2014; Revised 9 June 2014; Accepted 9 June 2014; Published 16 July 2014
Academic Editor: Dumitru Baleanu
Copyright © 2014 Seyma Tuluce Demiray 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.
- J. M. Burgers, “A mathematical model illustrating the theory of turbulence,” Advances in Applied Mechanics, vol. 1, pp. 171–199, 1948.
- J. W. Cahn and J. E. Hilliard, “Free energy of a nonuniform system. I. Interfacial free energy,” The Journal of Chemical Physics, vol. 28, no. 2, pp. 258–267, 1958.
- A. Novick-Cohen, “The Cahn-Hilliard equation,” in Handbook of Differential Equations, Evolutionary Equations, vol. 4, Haifa, Israel, Elsevier, 2008.
- D. J. Korteweg and G. de Vires, “On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary wawes,” Philosophical Magazine, vol. 39, pp. 422–443, 1895.
- M. K. Fung, “KdV equation as an Euler-Poincare' equation,” Chinese Journal of Physics, vol. 35, no. 6, pp. 789–796, 1997.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differantial Equations, Wiley, New York, NY, USA, 1993.
- A. A. Kilbas, H. M. Srivastava, and J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science, New York, NY, USA, 2006.
- I. Podlubny, Fractional Differantial Equations, Academic Press, San Diego, Calif, USA, 1999.
- X.-J. Yang, D. Baleanu, Y. Khan, and S. T. Mohyud-din, “Local fractional variational iteration method for diffusion and wave equations on cantor sets,” Romanian Journal of Physics, vol. 59, no. 1-2, pp. 36–48, 2014.
- X.-J. Yang and D. Baleanu, “Fractal heat conduction problem solved by local fractional variation iteration method,” Thermal Science, vol. 17, no. 2, pp. 625–628, 2013.
- X. J. Yang, H. M. Srivastava, J. H. He, and D. Baleanu, “Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives,” Physics Letters A, vol. 377, no. 28–30, pp. 1696–1700, 2013.
- X.-J. Yang, D. Baleanu, and J. He, “Transport equations in fractal porous media within fractional complex transform method,” Proceedings of the Romanian Academy A: Mathematics, Physics, Technical Sciences, Information Science, vol. 14, no. 4, pp. 287–292, 2013.
- A. Atangana, S. T. Demiray, and H. Bulut, “Modelling the nonlinear wave motion within the scope of the fractional calculus,” Abstract and Applied Analysis, vol. 2014, Article ID 481657, 7 pages, 2014.
- Y. Pandir, Y. Gurefe, and E. Misirli, “The extended trial equation method for some time fractional differential equations,” Discrete Dynamics in Nature and Society, Article ID 491359, 13 pages, 2013.
- Y. Pandir, “New exact solutions of the generalized Zakharov-Kuznetsov modified equal width equation,” Pramana, vol. 82, no. 6, pp. 949–964, 2014.
- H. Bulut, H. M. Baskonus, and Y. Pandir, “The modified trial equation method for fractional wave equation and time fractional generalized Burgers equation,” Abstract and Applied Analysis, vol. 2013, Article ID 636802, 8 pages, 2013.
- Y. Pandir and Y. A. Tandogan, “Exact solutions of the time-fractional Fitzhugh-Nagumo equation,” in Proceedings of the 11th International Conference on Numerical Analysis and Applied Mathematics, vol. 1558 of AIP Conference Proceedings, pp. 1919–1922, 2013.
- Y. Pandir, Y. Gurefe, and E. Misirli, “A multiple extended trial equation method for the fractional Sharma-Tasso-Olver equation,” in Proceedings of the 11th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM '13), vol. 1558 of AIP Conference Proceedings, pp. 1927–1930, 2013.
- H. Bulut, Y. Pandir, and H. M. Baskonus, “Symmetrical hyperbolic Fibonacci function solutions of generalized Fisher equation with fractional order,” AIP Conference Proceedings, vol. 1558, pp. 1914–1918, 2013.
- Y. A. Tandogan, Y. Pandir, and Y. Gurefe, “Solutions of the nonlinear differential equations by use of modified Kudryashov method,” Turkish Journal of Mathematics and Computer Science, Article ID 20130021, 7 pages, 2013.
- Y. Pandir, “Symmetric fibonacci function solutions of some nonlinear partial differantial equations,” Applied Mathematics Information Sciences, vol. 8, no. 5, pp. 2237–2241, 2014.
- R. Sahadevan and T. Bakkyaraj, “Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries equations,” Journal of Mathematical Analysis and Applications, vol. 393, no. 2, pp. 341–347, 2012.
- A. Bekir, Ö. Güner, and A. C. Cevikel, “Fractional complex transform and exp-function methods for fractional differential equations,” Abstract and Applied Analysis, vol. 2013, Article ID 426462, 8 pages, 2013.
- Z. Dahmani and M. Benbachir, “Solutions of the Cahn-Hilliard equation with time- and space-fractional derivatives,” International Journal of Nonlinear Science, vol. 8, no. 1, pp. 19–26, 2009.
- H. Jafari, H. Tajadodi, N. Kadkhoda, and D. Baleanu, “Fractional subequation method for Cahn-Hilliard and Klein-Gordon equations,” Abstract and Applied Analysis, vol. 2013, Article ID 587179, 5 pages, 2013.
- J. Hu, Y. Ye, S. Shen, and J. Zhang, “Lie symmetry analysis of the time fractional KdV-type equation,” Applied Mathematics and Computation, vol. 233, pp. 439–444, 2014.
- Y. Zhang, “Formulation and solution to time-fractional generalized Korteweg-de Vries equation via variational methods,” Advances in Difference Equations, vol. 2014, article 65, 12 pages, 2014.
- S. A. El-Wakil, E. M. Abulwafa, and M. A. Zahran, “Time-fractional KdV equation: formulation and solution using variational methods,” Nonlinear Dynamics, vol. 65, no. 1-2, pp. 55–63, 2011.
- G. W. Wang, T. Z. Xu, and T. Feng, “Lie symmetry analysis and explicit solutions of the time fractional fifth-order KdV equation,” PLoS ONE, vol. 9, no. 2, Article ID e88336, 2014.
- N. A. Kudryashov, “One method for finding exact solutions of nonlinear differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 6, pp. 2248–2253, 2012.
- J. Lee and R. Sakthivel, “Exact travelling wave solutions for some important nonlinear physical models,” Pramana—Journal of Physics, vol. 80, no. 5, pp. 757–769, 2013.
- P. N. Ryabov, D. I. Sinelshchikov, and M. B. Kochanov, “Application of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations,” Applied Mathematics and Computation, vol. 218, no. 7, pp. 3965–3972, 2011.