  We present two types of polynomials related to the Mittag-Leffler function
namely the fractional Hermite polynomial and the Mittag-Leffler polynomial. The
first modifies the Hermite polynomial and the second one is a refashioned
Laguerre polynomial. The fractional Hermite and the Mittag-Leffler polynomials
are used to solve {the Cauchy problems for} the fractional Fokker-Planck
equation where the fractional derivative is taken in the Caputo sense with
respect to time and/or space. The generating functions of these two kinds of
polynomials are also calculated and they indicate that these polynomials belong
to the Sheffer type.
