Polynomial Least Squares Method for Fractional Lane–Emden Equations

Bogdan Căruntu,Mădălina Paşca,Marioara Lăpădat,Constantin Bota

doi:10.3390/sym11040479

Bogdan Căruntu, Mădălina Paşca + Show 2 more

Open Access

https://doi.org/10.3390/sym11040479

Copy DOI

Abstract

This paper applies the Polynomial Least Squares Method (PLSM) to the case of fractional Lane-Emden differential equations. PLSM offers an analytical approximate polynomial solution in a straightforward way. A comparison with previously obtained results proves how accurate the method is.

Highlights

The equation analyzed in this article was published at the end of the 19th century by Jonathan
In the decades that followed, the equation Lane-Emden raised the interest of many researchers who used different methods to determine numerical or analytical solution for the equation
The above fractional Lane-Emden equation can demonstrate various phenomena arising in mathematical physics and astrophysics

Summary

Introduction

The equation analyzed in this article was published at the end of the 19th century by Jonathan. In the decades that followed, the equation Lane-Emden raised the interest of many researchers who used different methods to determine numerical or analytical solution for the equation. In this paper we start by considering the following Lane-Emden Fractional Differential. The above fractional Lane-Emden equation can demonstrate various phenomena arising in mathematical physics and astrophysics. In recent years many researchers sought solutions for this type of equation. Depending on the values of the constants and functions involved in (1) and (2), there are several particular types of equations with important practical applications, e.g., thermionic currents, gravitational potential of the degenerate white-dwarf stars or isothermal gas spheres. Squares Method (PLSM) [17] which permits determination of analytical approximate polynomial solutions for problems of the type (1) and (2). In the second section we will compare approximate solutions obtained by using PLSM with corresponding approximate solutions obtained in previous studies by means of other methods

The Polynomial Least Squares Method

Application 1

Application 2

Application 3

Conclusions