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In this paper, the bifurcation and new exact solutions for the ( 2 + 1 $2+1$ )-dimensional conformable time-fractional Zoomeron equation are investigated by utilizing two reliable methods, which are generalized ( G ′ / G ) $(G'/G)$ -expansion method and the integral bifurcation method. The exact solutions of the ( 2 + 1 $2+1$ )-dimensional conformable time-fractional Zoomeron equation are obtained by utilizing the generalized ( G ′ / G ) $(G'/G)$ -expansion method, these solutions are classified as hyperbolic function solutions, trigonometric function solutions, and rational function solutions. Giving different parameter conditions, many integral bifurcations, phase portraits, and traveling wave solutions for the equation are obtained via the integral bifurcation method. Graphical representations of different kinds of the exact solutions reveal that the two methods are of significance for constructing the exact solutions of fractional partial differential equation.

Bifurcation and exact solutions for the ($2+1$)-dimensional conformable time-fractional Zoomeron equation