Analysis of a fractional predator–prey model with cannibalism and immatures’ hunting

The dynamic interplay among the prey species, the immature predator and the matured predator species, where the cannibalism in the predator species with the aspect of predation of the immature predators by the matured predators is appraised. Consequential to this cannibalism scenario, the young ones have to hunt themselves, and hence, the incorporation of hunting of the prey by the immature predators and its correspondence to their transition into the matured stage. Also, the efficacious nature of memory is explored by inculcating Caputo’s fractional order derivatives in lieu of ordinary derivatives. The constructed system’s applicability is proved. For the attainment of desirable population densities, the local and the global stability at the equilibrium points are surveyed, along with the conditions associated with Hopf bifurcation. Through numerical simulation, the dynamic behavior of the whole system is seen corresponding to the changes in the environmental parameters, thereby their importance pertaining to the memory effect. Cannibalism has a stabilizing impact on the system, while for a higher recollection ability, any impact of cannibalism vanishes; the reproduction capability from cannibalism is discussed in detail; the transition rate from the immature predators’ hunting unveils twice-occurring Hopf bifurcation for some numerical values of the memory effect.