Solitary and periodic wave solutions of higher-dimensional conformable time-fractional differential equations using the ( G ′ G , 1 G ) $( \frac{G'}{G},\frac{1}{G} ) $ -expansion method

In this paper, the two variables $( \frac{G'}{G},\frac{1}{G} ) $ -expansion method is applied to obtain new exact solutions with parameters of higher-dimensional nonlinear time-fractional differential equations (NTFDEs) in the sense of the conformable fractional derivative. To clarify the veracity of this method, it is implemented in nonlinear $(2+1)$ -dimensional time-fractional biological population (BP) model and nonlinear $(3+1)$ -dimensional KdV–Zakharov–Kuznetsov (KdV–ZK) equation with time-fractional derivative. When the parameters take some special values, the solitary and periodic solutions are obtained from the hyperbolic and trigonometric function solutions.