Fractional Artificial Neural Networks for Growth Models

TL;DR

This paper introduces a fractional artificial neural network approach to solve initial value problems in fractional growth models, including exponential and logistic models with periodic harvesting, implemented in R.

Contribution

The paper presents a novel neural network method for fractional differential equations, specifically tailored for growth models with periodic harvesting, using a discretization of the Caputo derivative.

Findings

The neural network accurately approximates solutions to fractional growth models.

Comparison shows the neural network's solutions closely match analytical solutions.

Implementation in R demonstrates practical applicability.

Abstract

In this paper we present a method to solve initial value problems for fractional growth models, such as generalizations of the exponential and logistic with periodic harvesting models. Using a discretization of the Caputo derivative we propose a fractional artificial neural network, which is implemented in the statistical software R. Moreover, we show examples where the analytical solutions and the approximation of the artificial neural network are compared.