On the fractional order space-time nonlinear equations arising in plasma physics

  • M A AbdouEmail author
Original Paper


In this study, the \(\exp (-\phi (\xi ))\)-expansion function method is considered for solving two classes of space-time fractional partial differential equations of very special interest. The two classes, namely the higher dimensional Kadomtsev–Petviashvili and Boussinesq equations, have a wide range applications in different areas of complex nonlinear physics such as plasma physics, fluid dynamics and nonlinear optics. As a result, the \(\exp (-\phi (\xi ))\)-expansion function method yields a different class of traveling solutions mapped to trigonometric functions, rational functions and hyperbolic functions. Also, the behavior of these solutions has been significantly affected by changing the values of fractional order where the obtained solutions go back to those obtained previously to the normal case, i.e.,\(\alpha =\beta =1\). Finally, our finding may be of wide relevance and helpful to better understand the main features and propagation of the nonlinear waves in fractal medium.


Fractional complex transform Modified \(\exp (-\phi (\xi ))\)-expansion function method Plasma physics Exact solutions 


02.90.+p 02.30.Jr 02.30.Mv 


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Copyright information

© Indian Association for the Cultivation of Science 2018

Authors and Affiliations

  1. 1.Physics Department, College of ScienceUniversity of BishaBishaKingdom of Saudi Arabia
  2. 2.Theoretical Research Group, Physics Department, Faculty of ScienceMansoura UniversityMansouraEgypt

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