The present paper reports the result of a study on eigenvalue approximation of the Airy fractional differential equation, using a new differential of fractional derivative called conformable fractional derivative. We have tried to present the approximate solution of the eigenvalue of Airy fractional differential equation (AFDE) on the right half-line and the left half-line with a turning point through applying the Adomian decomposition method. All numerical calculations in this manuscript were performed on a PC applying some programs written in Mathematica
