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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

    K. Hosseini

  2. Department of Mathematics and Computer, Art–Science Faculty, Eskisehir Osmangazi University, Eskisehir, Turkey

    A. Bekir

  3. Department of Mechanical Engineering, University of Guilan, Rasht, Iran

    R. Ansari

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  1. K. Hosseini
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  2. A. Bekir
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  3. R. Ansari
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Correspondence to A. Bekir.

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Hosseini, K., Bekir, A. & Ansari, R. Exact solutions of nonlinear conformable time-fractional Boussinesq equations using the \(\exp \left( { - \phi \left( \varepsilon \right)} \right)\)-expansion method. Opt Quant Electron 49, 131 (2017). https://doi.org/10.1007/s11082-017-0968-9

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