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

The spherical isothermal Lane-Emden equation is a second-order nonlinear differential equation that models many configurations in astrophysics. Using the fractal index technique and the power series expansion, we solve the fractional Lane-Emden equation involving the modified Riemann-Liouville derivative. The results indicate that the series converges over the range of radii 0≤ x < 2200 for a wide spread of values for the fractional parameter α. Comparison with the numerical solution reveals good agreement with a maximum relative error of 0.05.