  The paper studies the exact solution of two kinds of generalized
Fokker-Planck equations in which the integral kernels are given either by the
distributed order function $k_{1}(t) = \int_{0}^{1} t^{-\mu}/\Gamma(1- \mu)
d\mu$ or the distributed order Prabhakar function $k_{2}(\alpha, \gamma;
\lambda; t) = \int_{0}^{1} e^{-\gamma}_{\alpha, 1 - \mu}(\lambda; t) d\mu$,
where the Prabhakar function is denoted as $e^{-\gamma}_{\alpha, 1 -
\mu}(\lambda; t)$. Both of these integral kernels can be called the fading
memory functions and are the Stieltjes functions. It is also shown that their
Stieltjes character is enough to ensure the non-negativity of the mean square
values and higher even moments. The odd moments vanish. Thus, the solution of
generalized Fokker-Planck equations can be called the probability density
functions. We introduce also the Volterra-Prabhakar function and its
generalization which are involved in the definition of $k_{2}(\alpha, \gamma;
\lambda; t)$ and generated by it the probability density function $p_2(x, t)$.
