arXiv subjects

Mabel Tidball

Publications and source records attributed to Mabel Tidball.

3 recordsLinked to original sources

arXiv2021

Harvest management problem in a fractional logistic equation

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.

math.OC↗

arXiv2021

Necessary conditions to a fractional variational problem

In order to solve fractional variational problems, there exist two theorems of necessary conditions: an Euler-Lagrange equation which involves Caputo and Riemann-Liouville fractional derivatives, and other Euler-Lagrange equation that involves only Caputo derivatives. In this article, we make a comparison solving a particular fractional variational problem with both methods to obtain some conclusions about which method gives the optimal solution.

math.OC↗

arXiv2021

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

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.

math.DS↗