Approximate solution to the fractional Lane-Emden type equations

TL;DR

This paper introduces an approximate series solution method for fractional Lane-Emden equations, demonstrating its effectiveness and consistency with existing methods through various examples.

Contribution

It presents a novel series expansion approach for fractional Lane-Emden equations and establishes its equivalence with other established methods in the integer case.

Findings

The method produces accurate approximate solutions.

Results align with those from other established methods.

The recurrence relation simplifies solution construction.

Abstract

In this paper, approximate solutions for a class of fractional Lane - Emden type equations based on the series expansion method are presented. Various examples are introduced and discussed. The recurrence relation for the components of the approximate solution is constructed. In the standard integer order derivative, it is shown that the results are the same as those obtained by Adomian decomposition method, homotopy perturbation method, modified Laplace decomposition method and variational iteration method.