Abstract
In the present paper, we use efficient and simple algorithms of the fractional power series and Adomain polynomial methods that provide effective tools for solving such linear and nonlinear fractional differential equations in the sense of conformable derivative. The first method succeeded in finding the fractional power series solution for the Laguerre linear fractional differential equation with some important special cases. The second method is applied to predict and construct the fractional Adomain approximation solution of the general conformable Lane-Emden fractional differential equation with some interesting linear and nonlinear special cases with their graphs. Finally, the results show that the Adomain approximation solutions of those problems are stable at different values of α and assure that this way can be applied successfully for solving many linear and nonlinear fractional differential equations in conformable sense.