<p>In any ecosystem generalist predators are always found in the system. Animal social behaviour has piqued the interest of animal behaviorists and evolutionary biologists. Predators cause stress in their prey and can benefit ecosystems, but if they are overpopulated, they can also have a negative impact on biodiversity. This paper investigates the joint effects of hunting cooperation and fear in a generalist predator-prey system. In the real world, in addition to these ecological factors, prey and predator have memory for use of “where”, “what”and “when”. Thus, memory effects are also considered on population growth. System’s well-posedness is investigated mathematically. Steady states of the proposed system are rigorously analyzed. Additionally, the conditions of existence of Hopf bifurcation for coexistence equilibrium point are derived. The most fascinating finding in this study is the comparisons between the commensurate and incommensurate fractional-order systems numerically. The study obtains important biological findings regarding the effects of various memory strengths. Prey with weak memory experience inhibited growth due to predation fear, but as their memory strengthens, they overcome fear and grow faster. A strong memory of prey species as well as predator species sometimes can have a negative impact on their growth. Furthermore, the study finds that the existence of a population is influenced by both strong and weak memories, depending on the characteristics of the population.</p>