Numerical solution of the third order fractional differential equation is obtained by using DGJ (Daftardar-Gejii-Jafaris) method. Providing DGJ method converges, it is shown that obtained approximate solution is effective which is close to the exact solution or the exact solution. An example explained this method is presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. An example which shows the method is unsuitable and inconsistent is given.