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The \(\phi ^{6}\)-model expansion method for solving the nonlinear conformable time-fractional Schrödinger equation with fourth-order dispersion and parabolic law nonlinearity

  • Elsayed M. E. Zayed
  • Abdul-Ghani Al-Nowehy
Article

Abstract

The \(\phi ^{6}\)-model expansion method combined with the conformable time-fractional derivative is applied in this paper for finding many new exact solutions including Jacobi elliptic function solutions, solitary wave solutions, trigonometric function solutions and other solutions to the nonlinear conformable time-fractional Schrödinger equation with fourth-order dispersion and parabolic law nonlinearity. This method presents a wider applicability for handling the nonlinear partial differential equations. Comparing our results with the well-known results are given.

Keywords

The \(\phi ^{6}\)-model expansion method Conformable fractional derivative Jacobi elliptic function solutions Exact solutions Solitary wave solutions Other solutions Nonlinear Schrödinger equation 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics Department, Faculty of ScienceZagazig UniversityZagazigEgypt
  2. 2.Mathematics Department, Faculty of Education and ScienceTaiz UniversityTaizYemen

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