Harvest management problem in a fractional logistic equation

TL;DR

This paper investigates a fractional control problem for resource management modeled by a fractional logistic equation, developing solution techniques and comparing classical and fractional cases through numerical simulations.

Contribution

It introduces novel resolution methods for a singular fractional control problem and compares classical and fractional models via numerical analysis.

Findings

Fractional models provide different insights into resource dynamics.

New solution techniques for singular fractional control problems.

Numerical simulations highlight differences between classical and fractional cases.

Abstract

In this article, we study a fractional control problem that models the maximization of the profits obtained by exploiting a certain resource whose dynamics are governed by the fractional logistic equation. Due to the singularity of this problem, we develop different resolution techniques, both for the classical case and for the fractional case. In the last section we perform several numerical simulations to make a comparison between both cases.