Nonlinear Dynamics

, Volume 81, Issue 3, pp 1569–1574 | Cite as

Fractional Lie group method of the time-fractional Boussinesq equation

  • Hossein Jafari
  • Nematollah Kadkhoda
  • Dumitru Baleanu
Original Paper


Finding the symmetries of the nonlinear fractional differential equations is a topic which has many applications in various fields of science and engineering. In this manuscript, firstly, we are interested in finding the Lie point symmetries of the time-fractional Boussinesq equation. After that, by using the infinitesimal generators, we determine their corresponding invariant solutions.


Fractional differential equation  Lie group Time-fractional Boussinesq equation Riemann–Liouville derivative Group-invariant solutions 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Hossein Jafari
    • 1
    • 2
  • Nematollah Kadkhoda
    • 3
  • Dumitru Baleanu
    • 4
    • 5
  1. 1.Department of MathematicsUniversity of MazandaranBabolsarIran
  2. 2.Department of Mathematical SciencesUniversity of South Africa (UNISA)PretoriaSouth Africa
  3. 3.Department of Mathematics, Faculty of Basic SciencesBozorgmehr University of QaenatQaenatIran
  4. 4.Department of Mathematics, Faculty of Art and SciencesCankaya UniversityBalgatTurkey
  5. 5.Institute of Space SciencesMagurele, BucharestRomania

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