Project Euclid

References

• J. M. Burgers, “A mathematical model illustrating the theory of turbulence,” Advances in Applied Mechanics, vol. 1, pp. 171–199, 1948.
  Mathematical Reviews (MathSciNet): MR27195
  
• J. W. Cahn and J. E. Hilliard, “Free energy of a nonuniform sys-tem. 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.
  Mathematical Reviews (MathSciNet): MR2508166
  Digital Object Identifier: doi:10.1016/S1874-5717(08)00004-2
  
• 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\textquotesingle equation,” Chinese Journal of Physics, vol. 35, no. 6, pp. 789–796, 1997.
  Mathematical Reviews (MathSciNet): MR1613273
  
• K. S. Miller and B. Ross, An Introduction to the Fractional Cal-culus and Fractional Differantial Equations, Wiley, New York, NY, USA, 1993.
  Mathematical Reviews (MathSciNet): MR1219954
  
• A. A. Kilbas, H. M. Srivastava, and J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science, New York, NY, USA, 2006.
  Mathematical Reviews (MathSciNet): MR2218073
  
• I. Podlubny, Fractional Differantial Equations, Academic Press, San Diego, Calif, USA, 1999.
  Mathematical Reviews (MathSciNet): MR1658022
  
• 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.
  Mathematical Reviews (MathSciNet): MR3190242
  
• 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.
  Mathematical Reviews (MathSciNet): MR3062238
  Digital Object Identifier: doi:10.1016/j.physleta.2013.04.012
  
• 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.
  Mathematical Reviews (MathSciNet): MR3147127
  
• A. Atangana, S. T. Demiray, and H. Bulut, “Modelling the non-linear wave motion within the scope of the fractional calculus,” Abstract and Applied Analysis, vol. 2014, Article ID 481657, 7 pages, 2014.
  Mathematical Reviews (MathSciNet): MR3214433
  
• 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.
  Mathematical Reviews (MathSciNet): MR3071603
  
• 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 frac-tional generalized Burgers equation,” Abstract and Applied Analysis, vol. 2013, Article ID 636802, 8 pages, 2013.
  Mathematical Reviews (MathSciNet): MR3096833
  
• 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 equa-tion,” in Proceedings of the 11th International Conference of Num-erical 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 hyper-bolic 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 non-linear 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.
  Mathematical Reviews (MathSciNet): MR3178729
  
• 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.
  Mathematical Reviews (MathSciNet): MR2921677
  Zentralblatt MATH: l1245.35142
  Digital Object Identifier: doi:10.1016/j.jmaa.2012.04.006
  
• 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.
  Mathematical Reviews (MathSciNet): MR3064543
  Digital Object Identifier: doi:10.1155/2013/426462
  
• 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.
  Mathematical Reviews (MathSciNet): MR2557974
  Zentralblatt MATH: l1179.35263
  
• H. Jafari, H. Tajadodi, N. Kadkhoda, and D. Baleanu, “Fractional subequation method for Cahn-Hilliard and Klein-Gor-don equations,” Abstract and Applied Analysis, vol. 2013, Article ID 587179, 5 pages, 2013.
  Mathematical Reviews (MathSciNet): MR3034884
  Digital Object Identifier: doi:10.1155/2013/587179
  
• 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.
  Mathematical Reviews (MathSciNet): MR3214998
  Digital Object Identifier: doi:10.1016/j.amc.2014.02.010
  
• 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-frac-tional KdV equation: formulation and solution using variational methods,” Nonlinear Dynamics, vol. 65, no. 1-2, pp. 55–63, 2011.
  Mathematical Reviews (MathSciNet): MR2812008
  Digital Object Identifier: doi:10.1007/s11071-010-9873-5
  
• G. W. Wang, T. Z. Xu, and T. Feng, “Lie symmetry analysis and explicit solutions of the time fractional fifth-order KdV equa-tion,” 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.
  Mathematical Reviews (MathSciNet): MR2877672
  Zentralblatt MATH: l1250.35055
  Digital Object Identifier: doi:10.1016/j.cnsns.2011.10.016
  
• 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. \endinput
  Mathematical Reviews (MathSciNet): MR2851496
  Zentralblatt MATH: l1246.35015
  Digital Object Identifier: doi:10.1016/j.amc.2011.09.027