Analytical solution to the conformable fractional Lane-Emden type equations arising in astrophysics

Abstract

Lane-Emden equations have many applications in physical science and so make great attention to researchers. In most cases there is are no exact solutions to these equations and only approximate solutions could be performed. This paper introduces analytical solutions to Lane-Emden type equations using the fractional Adomian decomposition method. We solve six examples related to astrophysical and physical problems. The approximate solutions are derived in the form of a divergent series. In the case of the fractional parameter equal one, the integer order, we obtained the same results as obtained by the method of Adomian decomposition.