Artificial Neural Network Modeling of the Conformable Fractional Isothermal Gas Spheres

TL;DR

This paper introduces an ANN-based computational method to simulate conformable fractional isothermal gas spheres, a model relevant in astrophysics, demonstrating high accuracy compared to analytical solutions across various fractional parameters.

Contribution

The study presents a novel application of artificial neural networks to model conformable fractional isothermal gas spheres, extending traditional methods with a data-driven approach.

Findings

ANN accurately simulates fractional isothermal gas spheres

Results match analytical solutions across fractional parameters

Mass-radius and density profiles are effectively computed

Abstract

The isothermal gas sphere is a particular type of Lane-Emden equation and is used widely to model many problems in astrophysics like stars, star clusters, and the formation of galaxies. In this paper, we present a computational scheme to simulate the conformable fractional isothermal gas sphere using an artificial neural network (ANN) technique and compare the obtained results with the analytical solution deduced using the Taylor series. We performed our calculations, trained the ANN, and tested it using a wide range of the fractional parameter. Besides the Emden functions, we calculated the mass-radius relations and the density profiles of the fractional isothermal gas spheres. The results obtained provided that ANN could perfectly simulate the conformable fractional isothermal gas spheres.