Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013, Article ID 846283, 6 pages
http://dx.doi.org/10.1155/2013/846283
Research Article

Solution of Nonlinear Space-Time Fractional Differential Equations Using the Fractional Riccati Expansion Method

1Department of Mathematics, Faculty of Science, Assiut University, New Valley Branch, El-Kharja 72511, Egypt
2Department of Mathematics, Faculty of Science, Northern Border University, Arar 91431, Saudi Arabia
3Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Khartoum, 11111 Khartoum, Sudan

Received 19 June 2013; Accepted 2 December 2013

Academic Editor: Andrzej Swierniak

Copyright © 2013 Emad A.-B. Abdel-Salam and Eltayeb A. Yousif. 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 [18 citations]

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

  • S. A. El-Wakil, and Essam M. Abulwafa, “Formulation and solution of space–time fractional Boussinesq equation,” Nonlinear Dynamics, vol. 80, no. 1-2, pp. 167–175, 2014. View at Publisher · View at Google Scholar
  • Wei Li, Huizhang Yang, and Bin He, “Exact Solutions of Fractional Burgers and Cahn-Hilliard Equations Using Extended Fractional Riccati Expansion Method,” Mathematical Problems in Engineering, vol. 2014, pp. 1–9, 2014. View at Publisher · View at Google Scholar
  • E. A.-B. Abdel-Salam, E. A. Yousif, Y. A. S. Arko, and E. A. E. Gumma, “Solution of Moving Boundary Space-Time Fractional Burger’s Equation,” Journal of Applied Mathematics, vol. 2014, pp. 1–8, 2014. View at Publisher · View at Google Scholar
  • Constantin Bota, and Bogdan Căruntu, “Approximate Analytical Solutions of the Regularized Long Wave Equation Using the Optimal Homotopy Perturbation Method,” The Scientific World Journal, vol. 2014, pp. 1–6, 2014. View at Publisher · View at Google Scholar
  • Sara H. M. Hamed, Eltayeb A. Yousif, and Arbab I. Arbab, “Analytic and Approximate Solutions of the Space-Time Fractional Schrödinger Equations by Homotopy Perturbation Sumudu Transform Method,” Abstract and Applied Analysis, vol. 2014, pp. 1–13, 2014. View at Publisher · View at Google Scholar
  • Emad A-B. Abdel-Salam, and Elzain A.E. Gumma, “Analytical solution of nonlinear space-time fractional differential equations using the improved fractional Riccati expansion method,” Ain Shams Engineering Journal, vol. 6, no. 2, pp. 613–620, 2015. View at Publisher · View at Google Scholar
  • Emad A.-B. Abdel-Salam, and Gamal F. Hassan, “Multi-wave solutions of the space–time fractional Burgers and Sharma–Tasso–Olver equations,” Ain Shams Engineering Journal, 2015. View at Publisher · View at Google Scholar
  • Emad A.-B. Abdel-Salam, and Zeid I. A. Al-Muhiameed, “Analytic Solutions of the Space-Time Fractional Combined KdV-mKdV Equation,” Mathematical Problems in Engineering, vol. 2015, pp. 1–6, 2015. View at Publisher · View at Google Scholar
  • Emad Abdel-Baki Abdel-Salam, and Gamal Fargahly Hassan, “Multiwave solutions of fractional 4th and 5th order Burgers equations,” Turkish Journal of Physics, vol. 39, no. 3, pp. 227–241, 2015. View at Publisher · View at Google Scholar
  • E. A-B. Abdel-Salam, and M. I. Nouh, “Approximate Solution to the Fractional Second-Type Lane-Emden Equation,” Astrophysics, 2016. View at Publisher · View at Google Scholar
  • Hossein Aminikhah, Amir Hosein Refahi Sheikhani, and Hadi Rezazadeh, “Approximate analytical solutions of distributed order fractional Riccati differential equation,” Ain Shams Engineering Journal, 2016. View at Publisher · View at Google Scholar
  • Emad A-B. Abdel-Salam, and Gamal F. Hassan, “Study on the variable coefficient space–time fractional Korteweg de Vries equation,” Ain Shams Engineering Journal, 2016. View at Publisher · View at Google Scholar
  • Emad A-B. Abdel-Salam, Eltayeb A. Yousif, and Mostafa A. El-Aasser, “Analytical Solution of the Space-Time Fractional Nonlinear Schrödinger Equation,” Reports on Mathematical Physics, vol. 77, no. 1, pp. 19–34, 2016. View at Publisher · View at Google Scholar
  • Emad A-B. Abdel-Salam, and Gamal F. Hassan, “Solutions to Class of Linear and Nonlinear Fractional Differential Equations,” Communications in Theoretical Physics, vol. 65, no. 2, pp. 127–135, 2016. View at Publisher · View at Google Scholar
  • A. H. Bhrawy, “A space-time collocation scheme for modified anomalous subdiffusion and nonlinear superdiffusion equations,” European Physical Journal Plus, vol. 131, no. 1, 2016. View at Publisher · View at Google Scholar
  • Yusuf Pandir, and Ayse Yildirim, “Analytical approach for the fractional differential equations by using the extended tanh method,” Waves in Random and Complex Media, pp. 1–12, 2017. View at Publisher · View at Google Scholar
  • M. I. Nouh, and Emad A.-B. Abdel-Salam, “Approximate Solution to the Fractional Lane–Emden Type Equations,” Iranian Journal of Science and Technology, Transactions A: Science, 2017. View at Publisher · View at Google Scholar
  • E.A. Yousif, E.A-B. Abdel-Salam, and M.A. El-Aasser, “On the solution of the space–time fractional cubic nonlinear Schrödinger equation,” Results in Physics, 2017. View at Publisher · View at Google Scholar