In this work, we use two different techniques to discuss approximate analytical solutions for the time-fractional Fokker–Planck equation (TFFPE), namely the new iterative method (NIM) and the fractional power series method (FPSM). Stability analyses and truncation errors are studied using a procedure like the fundamental von Neumann stability analysis. Discretization is carried out numerically for TFFPE by the implicit finite difference and the Crank–Nicolson method. The techniques used in solving the TFFPE are simple and powerful enough to understand the numerical solutions of linear and nonlinear fractional differential equations. We discuss the approximate solutions obtained using the NIM and FPSM. This is explained by employing tables and shapes. The approximate solutions strongly converge to an accurate solution. All computations in this work were carried out using Maple 16.