- 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
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 491359, 13 pages
The Extended Trial Equation Method for Some Time Fractional Differential Equations
1Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey
2Department of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey
Received 21 February 2013; Revised 25 March 2013; Accepted 14 April 2013
Academic Editor: Ferhan M. Atici
Copyright © 2013 Yusuf Pandir 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. A. T. Machado, M. F. Silva, R. S. Barbosa et al., “Some applications of fractional calculus in engineering,” Mathematical Problems in Engineering, vol. 2010, Article ID 639801, 34 pages, 2010.
- M. Dalir and M. Bashour, “Applications of fractional calculus,” Applied Mathematical Sciences, vol. 4, no. 21–24, pp. 1021–1032, 2010.
- 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.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, The Netherlands, 2006.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- B. Lu, “The first integral method for some time fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 395, no. 2, pp. 684–693, 2012.
- A. El-Kahlout, T. O. Salim, and S. El-Azab, “Exact solution of time fractional partial differential equation,” Applied Mathematical Sciences, vol. 2, no. 49–52, pp. 2577–2590, 2008.
- 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.
- M. Dehghan, J. Manafian, and A. Saadatmandi, “Solving nonlinear fractional partial differential equations using the homotopy analysis method,” Numerical Methods for Partial Differential Equations, vol. 26, no. 2, pp. 448–479, 2010.
- G. Jumarie, “Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results,” Computers & Mathematics with Applications, vol. 51, no. 9-10, pp. 1367–1376, 2006.
- G. Jumarie, “Fractional Hamilton-Jacobi equation for the optimal control of nonrandom fractional dynamics with fractional cost function,” Journal of Applied Mathematics & Computing, vol. 23, no. 1-2, pp. 215–228, 2007.
- G. Jumarie, “Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions,” Applied Mathematics Letters, vol. 22, no. 3, pp. 378–385, 2009.
- Z. Z. Ganji, D. D. Ganji, A. D. Ganji, and M. Rostamian, “Analytical solution of time-fractional Navier-Stokes equation in polar coordinate by homotopy perturbation method,” Numerical Methods for Partial Differential Equations, vol. 26, no. 1, pp. 117–124, 2010.
- C.-S. Liu, “Trial equation method and its applications to nonlinear evolution equations,” Acta Physica Sinica, vol. 54, no. 6, pp. 2505–2509, 2005.
- C.-S. Liu, “Trial equation method for nonlinear evolution equations with rank inhomogeneous: mathematical discussions and applications,” Communications in Theoretical Physics, vol. 45, pp. 219–223, 2006.
- C.-S. Liu, “A new trial equation method and its applications,” Communications in Theoretical Physics, vol. 45, pp. 395–397, 2006.
- C.-S. Liu, “Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations,” Computer Physics Communications, vol. 181, no. 2, pp. 317–324, 2010.
- Y.-J. Cheng, “Classification of traveling wave solutions to the Vakhnenko equations,” Computers & Mathematics with Applications, vol. 62, no. 10, pp. 3987–3996, 2011.
- Y.-J. Cheng, “Classification of traveling wave solutions to the modified form of the Degasperis-Procesi equation,” Mathematical and Computer Modelling, vol. 56, no. 1-2, pp. 43–48, 2012.
- Y. Gurefe, A. Sonmezoglu, and E. Misirli, “Application of the trial equation method for solving some nonlinear evolution equations arising in mathematical physics,” Pramana, vol. 77, no. 6, pp. 1023–1029, 2011.
- Y. Gurefe, A. Sonmezoglu, and E. Misirli, “Application of an irrational trial equation method to high-dimensional nonlinear evolution equations,” Journal of Advanced Mathematical Studies, vol. 5, no. 1, pp. 41–47, 2012.
- Y. Pandir, Y. Gurefe, U. Kadak, and E. Misirli, “Classification of exact solutions for some nonlinear partial differential equations with generalized evolution,” Abstract and Applied Analysis, vol. 2012, Article ID 478531, 16 pages, 2012.
- Y. Gurefe, E. Misirli, A. Sonmezoglu, and M. Ekici, “Extended trial equation method to generalized nonlinear partial differential equations,” Applied Mathematics and Computation, vol. 219, no. 10, pp. 5253–5260, 2013.
- Y. Pandir, Y. Gurefe, and E. Misirli, “Classification of exact solutions to the generalized Kadomtsev-Petviashvili equation,” Physica Scripta, vol. 87, Article ID 025003, 12 pages, 2013.
- M. V. Demina and N. A. Kudryashov, “From Laurent series to exact meromorphic solutions: the Kawahara equation,” Physics Letters A, vol. 374, no. 39, pp. 4023–4029, 2010.
- N. A. Kudryashov and M. V. Demina, “Traveling wave solutions of the generalized nonlinear evolution equations,” Applied Mathematics and Computation, vol. 210, no. 2, pp. 551–557, 2009.
- A.-M. Wazwaz, “The variational iteration method for rational solutions for KdV, , Burgers, and cubic Boussinesq equations,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 18–23, 2007.
- P. Rosenau and J. M. Hyman, “Compactons: solitons with finite wavelengths,” Physical Review Letters, vol. 70, pp. 564–567, 1993.
- Z. Fu, S. Liu, S. Liu, and Q. Zhao, “New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations,” Physics Letters A, vol. 290, no. 1-2, pp. 72–76, 2001.