Dynamic analysis and optimal control of a fractional order fear-induced predator-prey model with stage structure and harvesting

This paper investigates a fractional-order predator-prey model incorporating fear effect, stage structure, harvesting, and Crowley-Martin type functional response. Firstly, the positivity and boundedness of the solutions are verified. Then, the sufficient conditions for the existence and stability of equilibria are presented. Next, the optimal control problem is studied by using Pontryagin’s maximum principle, and the formula for the optimal solution is derived. Finally, the theoretical results are validated through numerical simulations. The research shows that if fear effect reaches a certain peak, then the predator population will be almost at risk of extinction.