A fractional order cubic differential equation. Applications to natural resource management

TL;DR

This paper analyzes a fractional cubic differential equation, generalizing fractional logistic models, to develop simpler numerical methods, demonstrate solution existence and stability, and compare various logistic models for natural resource management.

Contribution

It introduces a generalized fractional cubic differential equation, proves solution existence and stability, and compares numerical methods for fractional logistic models.

Findings

Existence and uniqueness of solutions established.

Stability analysis performed.

Numerical comparisons of logistic models conducted.

Abstract

An analysis of a fractional cubic differential equation is presented, which is a generalization of different versions of fractional logistic equations, in order to obtain simpler numerical methods that globalize and extend the results already obtained, and allow the comparison between several methods. The existence and uniqueness of the solution of the fractional cubic problem subject to an initial value are demonstrated, a stability analysis is performed and, based on the implementation of numerical methods, a comparison is made between the different logistic models.