  In the present article, an approach to find the exact solution of the
fractional Fokker-Planck equation is presented. It is based on transforming it
to a system of first-order partial differential equation via Hopf
transformation, together with implementing the extended unified method. On the
other hand, reduction of the fractional derivatives to non autonomous ordinary
derivative. Thus the fractional Fokker-Planck equation is reduced to non
autonomous classical ones. Some explicit solutions of the classical, fractional
time derivative Fokker-Planck equation, are obtained . It is shown that the
solution of the Fokker-Planck equation is bi-Gaussian's. It is found that high
friction coefficient plays a significant role in lowering the standard
deviation. Further, it is found the fractionality has stronger effect than
fractality. It is worthy to mention that the mixture of Gaussian's is a
powerful tool in machine learning. Further, when varying the order of the
fractional time derivatives, results to slight effects in the probability
distribution function. Also, it is shown that the mean and mean square of the
velocity vary slowly.
