Abstract
In the realm of spatio-temporal fractional dynamics in a predator–prey system, we investigate fractional solitary wave-like solutions using the conformable space–time fractional coupled diffusion equation. To achieve this goal, we utilize the fractional derivative wave transformation approach to convert the conformable space–time fractional coupled nonlinear partial differential equations into equivalent ordinary differential equations. Subsequently, employing the G′G expansion technique, we obtain exact solutions for the transformed coupled ordinary differential equations. With the aid of these solutions and the fractional wave transformation, we construct three distinct fractional solitary wave-like solutions, namely kink-type, periodic, and rational for the considered fractional diffusive predator–prey model. Furthermore, we explore the dynamic attributes of prey and predator population densities by manipulating the space and time fractional-order parameters. Our findings reveal a significant insight: an increase in the fractional order can lead to system stabilization and foster the coexistence of both prey and predator species.