Abstract
In this paper, a mathematical analysis of fractional order fishery model with stage structure for predator is carried out under the background of prey refuge and protected area. First, it is demonstrated that the solution exists and is unique. The paper aims to analyze predator-prey dynamics in a fishery model through the application of fractional derivatives. It is worth emphasizing that we explicitly examine how fractional derivatives affect the dynamics of the model. The existence of each equilibrium point and the stability of the system at the equilibrium point are proved. The theoretical results are proved by numerical simulation. Alternatively, allocate harvesting efforts within an improved model aimed at maximizing economic benefits and ecologically sustainable development. The ideal solution is obtained by applying Pontryagin’s optimal control principle. A large number of numerical simulations show that the optimal control scheme can realize the sustainable development of the ecosystem.
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