Approximate Solution to the Fractional Second-Type Lane-Emden Equation

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.