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