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 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.
