Exact solutions of nonlinear conformable time-fractional Boussinesq equations using the \(\exp \left( { - \phi \left( \varepsilon \right)} \right)\)-expansion method

  • K. Hosseini
  • A. Bekir
  • R. Ansari


Nonlinear fractional Boussinesq equations are considered as an important class of fractional differential equations in mathematical physics. In this article, a newly developed method called the \(\exp \left( { - \phi \left( \varepsilon \right)} \right)\)-expansion method is utilized to study the nonlinear Boussinesq equations with the conformable time-fractional derivative. Different forms of solutions, including the hyperbolic, trigonometric and rational function solutions are formally extracted. The method suggests a useful and efficient technique to look for the exact solutions of a wide range of nonlinear fractional differential equations.


Nonlinear Boussinesq equations Conformable time-fractional derivative \(\text{Exp}\left( { - \phi \left( \varepsilon \right)} \right)\)-expansion method Hyperbolic, trigonometric and rational function solutions 


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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Rasht BranchIslamic Azad UniversityRashtIran
  2. 2.Department of Mathematics and Computer, Art–Science FacultyEskisehir Osmangazi UniversityEskisehirTurkey
  3. 3.Department of Mechanical EngineeringUniversity of GuilanRashtIran

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