The extended-$$\left( \frac{G'}{G}\right)$$-expansion method and new exact solutions for the conformable space-time fractional diffusive predator-prey system

This paper explores the dynamics of the conformable space-time fractional diffusive predator-prey system using the extended-[Formula: see text]-expansion method. By incorporating negative exponents into the solution process, the study uncovers a broader set of exact solutions, providing deeper insights into the system's behavior. The analysis reveals how the solutions' singularities shift in response to variations in the fractional orders, with a movement towards the boundary as the fractional order decreases and towards the angle bisector of space-time as it approaches 1. Additionally, the paper identifies chaotic phenomena that emerge in the triangular solution when the fractional order is near 0.7, highlighting the sensitivity of the system to small changes in this range. Through graphical representations and solution analysis, the paper demonstrates how these fractional-order dynamics influence predator-prey interactions, offering valuable contributions to both mathematical biology and the study of fractional differential equations in complex systems.