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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 839613, 7 pages
Solutions of Fractional Konopelchenko-Dubrovsky and Nizhnik-Novikov-Veselov Equations Using a Generalized Fractional Subequation Method
1School of Mathematical Sciences, Dezhou University, Dezhou 253023, China
2The Center of Data Processing and Analyzing, Dezhou University, Dezhou 253023, China
Received 13 July 2013; Accepted 8 August 2013
Academic Editor: Juan J. Trujillo
Copyright © 2013 Yanqin Liu and Limei Yan. 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. 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. M. Kolwankar and A. D. Gangal, “Local fractional Fokker-Planck equation,” Physical Review Letters, vol. 80, no. 2, pp. 214–217, 1998.
- G. C. Wu, “A fractional variational iteration method for solving fractional nonlinear differential equations,” Computers & Mathematics with Applications, vol. 61, no. 8, pp. 2186–2190, 2011.
- H. G. Sun and W. Chen, “Fractal derivative multi-scale model of fluid particle transverse accelerations in fully developed turbulence,” Science in China, Series E, vol. 52, no. 3, pp. 680–683, 2009.
- W. Chen and H. G. Sun, “Multiscale statistical model of fully-developed turbulence particle accelerations,” Modern Physics Letters B, vol. 23, no. 3, pp. 449–452, 2009.
- J. Cresson, “Scale calculus and the Schrödinger equation,” Journal of Mathematical Physics, vol. 44, no. 11, pp. 4907–4938, 2003.
- 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.
- S. W. Wang and M. Y. Xu, “Axial Couette flow of two kinds of fractional viscoelastic fluids in an annulus,” Nonlinear Analysis. Real World Applications, vol. 10, no. 2, pp. 1087–1096, 2009.
- X. Y. Jiang and M. Y. Xu, “The time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems,” Physica A, vol. 389, no. 17, pp. 3368–3374, 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.
- 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, “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.
- H. A. Ghany and M. S. Mohammed, “White noise functional solutions for Wick-type stochastic fractional KdV-Burgers-Kuramoto equations,” Chinese Journal of Physics, vol. 50, no. 4, pp. 619–627, 2012.
- M. L. Wang, “Solitary wave solutions for variant Boussinesq equations,” Physics Letters A, vol. 199, no. 3-4, pp. 169–172, 1995.
- S. Zhang and H.-Q. Zhang, “Fractional sub-equation method and its applications to nonlinear fractional PDEs,” Physics Letters A, vol. 375, no. 7, pp. 1069–1073, 2011.
- H. Jafari, H. Tajadodi, N. Kadkhoda, and D. Baleanu, “Fractional sub-equation method for Cahn-Hilliard and Klein-Gordon equations,” Abstract and Applied Analysis, vol. 2012, Article ID 587179, 5 pages, 2013.
- B. Tang, Y. He, L. Wei, and X. Zhang, “A generalized fractional sub-equation method for fractional differential equations with variable coefficients,” Physics Letters A, vol. 376, no. 38-39, pp. 2588–2590, 2012.
- S. M. Guo, L. Q. Mei, Y. Li, and Y. Sun, “The improved fractional sub-equation method and its applications to the space-time fractional differential equations in fluid mechanics,” Physics Letters A, vol. 376, no. 4, pp. 407–411, 2012.
- J. P. Zhao, B. Tang, S. Kumar, and Y. R. Hou, “The extended fractional subequation method for nonlinear fractional differential equations,” Mathematical Problems in Engineering, vol. 2012, Article ID 924956, 11 pages, 2012.
- H. A. Ghany, “Exact solutions for stochastic generalized hirota-satsuma coupled KdV equations,” Chinese Journal of Physics, vol. 49, no. 4, pp. 926–940, 2011.
- A. H. Ghany, A. S. O. El Bab, A. M. Zabel, and A.-A. Hyder, “The fractional coupled Kdv equations: exact solutions and white noise functional approach,” Chinese Physics B, vol. 22, no. 8, Article ID 080501.
- S. Zhang, “Exp-function method for Riccati equation and new exact solutions with two arbitrary functions of -dimensional Konopelchenko-Dubrovsky equations,” Applied Mathematics and Computation, vol. 216, no. 5, pp. 1546–1552, 2010.
- B.-C. Shin, M. T. Darvishi, and A. Barati, “Some exact and new solutions of the Nizhnik-Novikov-Vesselov equation using the Exp-function method,” Computers & Mathematics with Applications, vol. 58, no. 11-12, pp. 2147–2151, 2009.