  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.
