Abstract An approach to find the exact solution of ordinary, fractal and
fractional Fokker-Planck equation FPE, based on transforming it to a
system of first-order PDEs, together with using the extended unified
method, is presented. Reduction of the fractal and fractional
derivatives to the classical on's with time-dependent coefficient is
performed via similarity transformations. Some explicit solutions of the
classical, fractal and fractional time derivative FPE, are obtained . It
is shown that the solution of the FPE is mixed Gaussian's. It is worthy
to mention that the mixture of Gaussians is a powerful tool in machine
learning. Further,it is found that the friction coefficient plays a
significant role in lowering the magnitude of the distribution function.
While changing the order of the fractal and fraction time derivative has
a slight effects and the mean and mean square of the velocity vary
slowly.