Predator-incited fear weakened by infertility of prey in a prey–predator model with memory effect

This paper focuses on the construction along with investigation of a novel prey–predator model incorporating prey infertility and the integration of prey infertility with predator-incited fear. The model is built upon a basic prey–predator model, featuring a Michaelis–Menten response. Subsequently, fear effect is introduced to the model, followed by the integration of prey infertility into the concept of logistic growth. Finally, the prey infertility rate is included in the fear effect term. The system is formulated using fractional differential equations. This study covers the well-posedness, stability and Hopf bifurcation analysis of the model, conducting detailed numerical examinations together with biological interpretations. Pioneering and original results are achieved in terms of including the concept of prey infertility into the prey–predator model and considering it together with other biological facts, and incorporating the memory effect using fractional derivatives within the model.