Approximate Solution to the Fractional Second Type Lane-Emden Equation

TL;DR

This paper introduces an approximate analytical method using fractal index and series expansion to solve the fractional Lane-Emden equation, showing good agreement with numerical solutions across various fractional parameters.

Contribution

It presents a novel analytical approach for solving the fractional Lane-Emden equation involving modified Riemann-Liouville derivatives.

Findings

Series converges over a wide radius range.

Maximum relative error with numerical solution is 0.05.

Method effectively models astrophysical configurations.

Abstract

The spherical isothermal Lane-Emden equation is a second order non-linear differential equation that model many configurations in astrophysics. In the present paper and based on the fractal index technique and the series expansion, the fractional lane-Emden equation involving modified Riemann-Liouville derivative is solved. The results indicate that, the series converges for the radius range with fractional parameter spreads over a wide range of the fractional parameter . Comparison with the numerical solution revealed a good agreement with a maximum relative error 0.05.