OPTIMAL CONTROL POLICY APPLIED TO A PEST MANAGEMENT

Abstract

This work aims to present the fractional pest management model. The fractional Caputo derivative is employed. Fundamental properties of the considered model involving its equilibria, as well as the existence and boundedness of the solutions, are investigated. Furthermore, optimal control theory is used to determine a cost function and the best economic costs. This is achieved through the maximum principle of Pontryagin, which characterizes the optimal solution analytically, and then computes the optimal solution numericallyby employing a forward-backward method. Finally, some numerical simulations and their graphical representations are provided for a better insight into the results of the suggestedmodel.