<p>This study investigates the interaction between two populations, prey and predator, utilizing an enhanced Leslie-Gower model that incorporates the impact of fear on the prey population. The effect of memory on the model dynamical behavior is incorporated through the application of the Caputo fractional derivative, a widely recognized fractional operator. By applying the analytical approaches, the dynamic behaviour of the considered system is investigated, including stability and bifurcation. We identify requirements for the fixed points of the suggested prey-predator models’ local asymptotic stability. We used a numerical method to show the resulting system. We conducted comprehensive numerical simulations to validate the theoretical findings. Graphical representations are presented for the model, which includes a wide range of fractional-order values. The findings indicate that the functional response and level of fear are crucial in influencing the dynamics of the model.</p>