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

Abstract

Abstract In this paper, the two variables (G′G,1G) $( \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) $(2+1)$-dimensional time-fractional biological population (BP) model and nonlinear (3+1) $(3+1)$-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.

Keywords

• ( G ′ G , 1 G ) $( \frac{G'}{G}, \frac{1}{G})$ -expansion method
• Conformable fractional derivative
• Exact solutions
• ( 2 + 1 ) $(2+1)$ -dimensional time-fractional biological population model
• ( 3 + 1 ) $(3+1)$ -dimensional time-fractional KdV–Zakharov–Kuznetsov equation