Abstract
In this paper, the traditional separation method of variables is improved by fixing a part of the variables called the separation method of semi-fixed variables. By using this improved method, the time-fractional Fokker–Planck equation with external force field is studied. Some new exact solutions and dynamical properties of the equation are investigated in various external potential functions such as linear potential, harmonic potential, logarithmic potential, exponential potential, and quartic potential. Some interesting dynamical behaviors and phenomena are discovered. The profiles of several representative exact solutions are illustrated by 3D-graphs and 2D-graphs
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