Modeling Fractional Polytropic Gas Spheres Using Artificial Neural Network

TL;DR

This paper introduces a neural network-based computational method to solve fractional Lane-Emden differential equations, which model various astrophysical and physical phenomena, demonstrating high accuracy and efficiency compared to traditional approaches.

Contribution

It presents a novel ANN-based approach for solving fractional Lane-Emden equations, extending neural network applications to complex astrophysical differential equations.

Findings

The ANN method accurately solves fractional Lane-Emden equations.

The approach outperforms traditional methods in efficiency and accuracy.

Validated on multiple polytropic indices with results matching exact solutions.

Abstract

Lane-Emden differential equations describe different physical and astrophysical phenomena that include forms of stellar structure, isothermal gas spheres, gas spherical cloud thermal history, and thermionic currents. This paper presents a computational approach to solve the problems related to fractional Lane-Emden differential equations based on neural networks. Such a solution will help solve the fractional polytropic gas spheres problems which have different applications in physics, astrophysics, engineering, and several real-life issues. We used Artificial Neural Network (ANN) framework in its feedforward back propagation learning scheme. The efficiency and accuracy of the presented algorithm are checked by testing it on four fractional Lane-Emden equations and compared with the exact solutions for the polytopic indices n=0,1,5 and those of the series expansions for the polytropic index n=3. The results we obtained prove that using the ANN method is feasible, accurate, and may outperform other methods.