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Abstract
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In this article, a new version of the trial equation method is suggested. This method allows new exact solutions of the nonlinear partial differential equations. The developed method is applied to unstable nonlinear fractional-order Schrodinger equation in fractional time derivative derivative form of order . Some exact solutions of the fractional-order fractional PDE are attained by employing the new powerful expansion approach using by beta-fractional derivative which are used to get many solitary wave solutions by changing various parameters. New exact solutions are expressed with rational hyperbolic function solutions, rational trigonometric function solutions, 1-soliton solutions, dark soliton solitons and rational function solutions. We can say that unstable nonlinear Schrodinger equation exist different dynamical behaviors. In addition, the physical behaviors of these new exact solution are given with two and three dimensional graphs.
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