  We investigate a possibility to describe the non-Debye relaxation processes
using the Volterra-type equations with kernels given by the Prabhakar functions
with the upper parameter $\nu$ being negative. Proposed integro-differential
equations mimic the fading memory effects and are explicitly solved using the
umbral calculus and the Laplace transform methods. Both approaches lead to the
same results valid for admissible domain of the parameters $\alpha$, $\mu$ and
$\nu$ characterizing the Prabhakar function. For the special case $\alpha\in
(0,1]$, $\mu=0$ and $\nu=-1$ we recover the Cole-Cole model, in general having
a residual polarization. We also show that our scheme gives results equivalent
to those obtained using the stochastic approach to relaxation phenomena merged
with integral equations involving kernels given by the Prabhakar functions with
the positive upper parameter.
