Study of memory-dependent dynamics of a predator-prey model with hyperbolic mortality

This paper employs the Caputo fractional derivative to analyze a fractional-order prey-predator model distinguished by hyperbolic mortality, incorporating memory effects to augment the realism of species interactions. According to fixed point theory, it is proven that the system is well-posed ensuring the existence, uniqueness, positivity, and boundedness of the solution. Local stability is studied using the Jacobian matrix and fractional-order stability criteria. We conduct numerical simulations to corroborate the theoretical findings, and an error analysis utilizing step-size refinement demonstrates that the numerical scheme converges and is precise. Also, a sensitivity analysis is done to see how important parameters affect the dynamics of the system.