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The Scientific World Journal
Volume 2014, Article ID 489495, 10 pages
http://dx.doi.org/10.1155/2014/489495
Research Article

A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

1Department of Management Information Systems, School of Applied Sciences, Dumlupinar University, 43100 Kutahya, Turkey
2Department of Mathematics Education, Education Faculty, Yildiz Technical University, 34220 Istanbul, Turkey

Received 2 October 2013; Accepted 11 December 2013; Published 10 March 2014

Academic Editors: A. Kılıçman, S. S. Ray, and A. Secer

Copyright © 2014 Özkan Güner and Adem C. Cevikel. 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 [23 citations]

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

  • Omer Unsal, Ozkan Guner, Ahmet Bekir, and Adem C. Cevikel, “The (G′/G)-expansion method for the nonlinear time fractional differential equations,” vol. 1798, pp. 020167, . View at Publisher · View at Google Scholar
  • Ahmet Bekir, Özkan Güner, and Burcu Ayhan, “Exact solutions of some systems of fractional differential-difference equations,” Mathematical Methods in the Applied Sciences, 2014. View at Publisher · View at Google Scholar
  • Ahmet Bekir, and Ozkan Guner, “Analytical Approach for the Space-time Nonlinear Partial Differential Fractional Equation,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 15, no. 7-8, pp. 463–470, 2014. View at Publisher · View at Google Scholar
  • Ahmet Bekir, and Esin Aksoy, “Application of the Subequation Method to Some Differential Equations of Time-Fractional Order,” Journal Of Computational And Nonlinear Dynamics, vol. 10, no. 5, 2015. View at Publisher · View at Google Scholar
  • Ozkan Guner, “Singular and non-topological soliton solutions for nonlinear fractional differential equations,” Chinese Physics B, vol. 24, no. 10, pp. 100201, 2015. View at Publisher · View at Google Scholar
  • Ali H. Bhrawy, Taha M. Taha, and Jose A. Tenreiro Machado, “A review of operational matrices and spectral techniques for fractional calculus,” Nonlinear Dynamics, vol. 81, no. 3, pp. 1023–1052, 2015. View at Publisher · View at Google Scholar
  • Ozkan Guner, Ahmet Bekir, and Halis Bilgil, “A note on exp-function method combined with complex transform method applied to fractional differential equations,” Advances in Nonlinear Analysis, vol. 4, no. 3, pp. 201–208, 2015. View at Publisher · View at Google Scholar
  • Ozkan Guner, Ahmet Bekir, Yusuf Pandir, Ozkan Guner, Ahmet Bekir, and Yusuf Pandir, “Solving Nonlinear Space-time Fractional Differential Equations using the Exp-function Method,” Proceedings Of The International Conference Of Numerical Analysis And Applied Mathematics 2014 (Icnaam-2014), vol. 1648, 2015. View at Publisher · View at Google Scholar
  • Ozkan Guner, and Ahmet Bekir, “A novel method for nonlinear fractional differential equations using symbolic computation,” Waves in Random and Complex Media, pp. 1–8, 2016. View at Publisher · View at Google Scholar
  • Ahmet Bekir, Ozkan Guner, Burcu Ayhan, and Adem C. Cevikel, “Exact Solutions for Fractional Differential-Difference Equations by (G '/G)-Expansion Method with Modified Riemann-Liouville Derivative,” Advances In Applied Mathematics And Mechanics, vol. 8, no. 2, pp. 293–305, 2016. View at Publisher · View at Google Scholar
  • Ozkan Guner, and Ahmet Bekir, “Bright and dark soliton solutions for some nonlinear fractional differential equations,” Chinese Physics B, vol. 25, no. 3, pp. 030203, 2016. View at Publisher · View at Google Scholar
  • Ozkan Guner, and Ahmet Bekir, “On the concept of exact solution for nonlinear differential equations of fractional-order,” Mathematical Methods in the Applied Sciences, 2016. View at Publisher · View at Google Scholar
  • Ozkan Guner, Hasan Atik, and Alzhanov Aytugan Kayyrzhanovich, “New exact solution for space-time fractional differential equations via (G′/G)-expansion method,” Optik - International Journal for Light and Electron Optics, 2016. View at Publisher · View at Google Scholar
  • Ozkan Guner, Ahmet Bekir, and Ömer Ünsal, “Two reliable methods for solving the time fractional Clannish Random Walker's Parabolic equation,” Optik - International Journal for Light and Electron Optics, vol. 127, no. 20, pp. 9571–9577, 2016. View at Publisher · View at Google Scholar
  • Ozkan Guner, and Hasan Atik, “Soliton solution of fractional-order nonlinear differential equations based on the exp-function method,” Optik - International Journal for Light and Electron Optics, vol. 127, no. 20, pp. 10076–10083, 2016. View at Publisher · View at Google Scholar
  • Esin Aksoy, Melike Kaplan, and Ahmet Bekir, “Exponential rational function method for space–time fractional differential equations,” Waves in Random and Complex Media, pp. 1–10, 2016. View at Publisher · View at Google Scholar
  • Ahmet Bekir, Mohammad Mirzazadeh, Ozkan Guner, and Ömer Ünsal, “Applications of fractional complex transform and (Formula presented)-expansion method for time-fractional differential equations,” Journal of Applied Analysis and Computation, vol. 6, no. 1, pp. 131–144, 2016. View at Publisher · View at Google Scholar
  • Ozkan Guner, “Exp-Function Method and Fractional Complex Transform for Space-Time Fractional KP-BBM Equation,” Communications in Theoretical Physics, vol. 68, no. 2, pp. 149, 2017. View at Publisher · View at Google Scholar
  • Ahmet Bekir, Ozkan Guner, and Adem Cevikel, “The exp-function method for some time-fractional differential equations,” IEEE/CAA Journal of Automatica Sinica, vol. 4, no. 2, pp. 315–321, 2017. View at Publisher · View at Google Scholar
  • Alper Korkmaz, “Exact solutions of space-time fractional EW and modified EW equations,” Chaos, Solitons & Fractals, vol. 96, pp. 132–138, 2017. View at Publisher · View at Google Scholar
  • 亚东 王, “The Exp(-Φ(ξ)) Method for the Nonlinear Time Fractional Differential Equations,” Advances in Applied Mathematics, vol. 06, no. 04, pp. 515–522, 2017. View at Publisher · View at Google Scholar
  • Saima Arshed, and Misbah Sadia, “($$\frac{G^{'}}{G^{2}}$$G′G2)-Expansion method: new traveling wave solutions for some nonlinear fractional partial differential equations,” Optical and Quantum Electronics, vol. 50, no. 3, 2018. View at Publisher · View at Google Scholar
  • Ozkan Guner, “New exact solutions to the space–time fractional nonlinear wave equation obtained by the ansatz and functional variable methods,” Optical and Quantum Electronics, vol. 50, no. 1, 2018. View at Publisher · View at Google Scholar