About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 947986, 8 pages
http://dx.doi.org/10.1155/2013/947986
Research Article

The Time-Fractional Coupled-Korteweg-de-Vries Equations

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2Department of Mathematical Engineering, Yildiz Technical University, Davutpasa, 34210 Istanbul, Turkey

Received 5 January 2013; Accepted 7 February 2013

Academic Editor: Mustafa Bayram

Copyright © 2013 Abdon Atangana and Aydin Secer. 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.

Citations to this Article [29 citations]

The following is the list of published articles that have cited the current article.

  • Abdon Atangana, and S. C. Oukouomi Noutchie, “Two-Dimension Hydrodynamic Dispersion Equation with Seepage Velocity and Dispersion Coefficient as Function of Space and Time,” Abstract and Applied Analysis, vol. 2013, pp. 1–7, 2013. View at Publisher · View at Google Scholar
  • Abdon Atangana, and Aydin Secer, “A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions,” Abstract and Applied Analysis, vol. 2013, pp. 1–8, 2013. View at Publisher · View at Google Scholar
  • Abdon Atangana, and Samir Brahim Belhaouari, “Solving Partial Differential Equation with Space- and Time-Fractional Derivatives via Homotopy Decomposition Method,” Mathematical Problems in Engineering, vol. 2013, pp. 1–9, 2013. View at Publisher · View at Google Scholar
  • Abdon Atangana, and Adem Kılıçman, “Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method,” Abstract and Applied Analysis, vol. 2013, pp. 1–9, 2013. View at Publisher · View at Google Scholar
  • Ai-Ming Yang, Carlo Cattani, Hossein Jafari, and Xiao-Jun Yang, “Analytical Solutions of the One-Dimensional Heat Equations Arising in Fractal Transient Conduction with Local Fractional Derivative,” Abstract and Applied Analysis, 2013. View at Publisher · View at Google Scholar
  • Daliang Zhao, and Yansheng Liu, “Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems,” The Scientific World Journal, vol. 2013, pp. 1–9, 2013. View at Publisher · View at Google Scholar
  • Abdon Atangana, and Adem Kilicman, “A Novel Integral Operator Transform and Its Application to Some FODE and FPDE with Some Kind of Singularities,” Mathematical Problems in Engineering, vol. 2013, pp. 1–7, 2013. View at Publisher · View at Google Scholar
  • Abdon Atangana, O. Aden Ahmed, and Necdet Bildik, “A Generalized Version of a Low Velocity Impact between a Rigid Sphere and a Transversely Isotropic Strain-Hardening Plate Supported by a Rigid Substrate Using the Concept of Noninteger Derivatives,” Abstract and Applied Analysis, vol. 2013, pp. 1–9, 2013. View at Publisher · View at Google Scholar
  • F. Ghomanjani, and A. V. Kamyad, “Bezier Curves Method for Fourth-Order Integrodifferential Equations,” Abstract and Applied Analysis, 2013. View at Publisher · View at Google Scholar
  • Abdon Atangana, and Adem Kiliçman, “A Possible Generalization of Acoustic Wave Equation Using the Concept of Perturbed Derivative Order,” Mathematical Problems in Engineering, vol. 2013, pp. 1–6, 2013. View at Publisher · View at Google Scholar
  • Abdon Atangana, and Adem Kiliçman, “The Use of Sumudu Transform for Solving Certain Nonlinear Fractional Heat-Like Equations,” Abstract and Applied Analysis, vol. 2013, pp. 1–12, 2013. View at Publisher · View at Google Scholar
  • Abdon Atangana, and Necdet Bildik, “Approximate Solution of Tuberculosis Disease Population Dynamics Model,” Abstract and Applied Analysis, vol. 2013, pp. 1–8, 2013. View at Publisher · View at Google Scholar
  • Abdon Atangana, and Adem Kilicman, “Analytical Solutions of the Space-Time Fractional Derivative of Advection D ispersion Equation,” Mathematical Problems in Engineering, 2013. View at Publisher · View at Google Scholar
  • Abdon Atangana, and Necdet Bildik, “Existence and Numerical Solution of the Volterra Fractional Integral Equations of the Second Kind,” Mathematical Problems in Engineering, vol. 2013, pp. 1–11, 2013. View at Publisher · View at Google Scholar
  • Abdon Atangana, and Alain H. Cloot, “Stability and convergence of the space fractional variable-order Schrodinge r equation,” Advances in Difference Equations, 2013. View at Publisher · View at Google Scholar
  • Abdon Atangana, “Convergence and stability analysis of a novel iteration method for fractional biological population equation,” Neural Computing and Applications, 2014. View at Publisher · View at Google Scholar
  • Devendra Kumar, Jagdev Singh, and Sunil Kumar, “Numerical computation of fractional multi-dimensional diffusion equations by using a modified homotopy perturbation method,” Journal of the Association of Arab Universities for Basic and Applied Sciences, 2014. View at Publisher · View at Google Scholar
  • Yingjia Guo, “The Stability of Solutions for a Fractional Predator-Prey System,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014. View at Publisher · View at Google Scholar
  • Shun-Qin Wang, Yong-Ju Yang, and Hassan Kamil Jassim, “Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014. View at Publisher · View at Google Scholar
  • Abdon Atangana, and Suares Clovis Oukouomi Noutchie, “On Multi-Laplace Transform for Solving Nonlinear Partial Differential Equations with Mixed Derivatives,” Mathematical Problems in Engineering, vol. 2014, pp. 1–9, 2014. View at Publisher · View at Google Scholar
  • Xiao-Jun Yang, Jordan Hristov, H. M. Srivastava, and Bashir Ahmad, “Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg-de Vries Equation,” Abstract and Applied Analysis, vol. 2014, pp. 1–10, 2014. View at Publisher · View at Google Scholar
  • Abdon Atangana, and Suares Clovis Noutchie Oukouomi, “Novel Approach for Dealing with Partial Differential Equations with Mixed Derivatives,” Abstract and Applied Analysis, vol. 2014, pp. 1–8, 2014. View at Publisher · View at Google Scholar
  • Chun-Guang Zhao, Ai-Min Yang, Hossein Jafari, and Ahmad Haghbin, “The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative,” Abstract and Applied Analysis, vol. 2014, pp. 1–5, 2014. View at Publisher · View at Google Scholar
  • Abdon Atangana, Aden Ahmed, and Suares Clovis Oukouomi Noutchie, “On the Hamilton-Jacobi-Bellman Equation by the Homotopy Perturbation Method,” Abstract and Applied Analysis, vol. 2014, pp. 1–8, 2014. View at Publisher · View at Google Scholar
  • Abdon Atangana, and Emile Franc Doungmo Goufo, “ Computational Analysis of the Model Describing HIV Infection of CD4 + T Cells ,” BioMed Research International, vol. 2014, pp. 1–7, 2014. View at Publisher · View at Google Scholar
  • Chunye Gong, Weimin Bao, Guojian Tang, Yuewen Jiang, and Jie Liu, “A Domain Decomposition Method for Time Fractional Reaction-Diffusion Equation,” The Scientific World Journal, vol. 2014, pp. 1–5, 2014. View at Publisher · View at Google Scholar
  • Abdon Atangana, Necdet Bildik, and S. C. Oukouomi Noutchie, “New Iteration Methods for Time-Fractional Modified Nonlinear Kawahara Equation,” Abstract and Applied Analysis, vol. 2014, pp. 1–9, 2014. View at Publisher · View at Google Scholar
  • Abdon Atangana, “On the Singular Perturbations for Fractional Differential Equation,” The Scientific World Journal, vol. 2014, pp. 1–9, 2014. View at Publisher · View at Google Scholar
  • Abdon Atangana, and P. D. Vermeulen, “Modelling the Aggregation Process of Cellular Slime Mold by the Chemical Attraction,” BioMed Research International, vol. 2014, pp. 1–9, 2014. View at Publisher · View at Google Scholar