  We investigate the stochastic processes obtained as the fractional
Riemann-Liouville integral of order $\alpha \in (0,1)$ of Gauss-Markov
processes. The general expressions of the mean, variance and covariance
functions are given. Due to the central rule, for the fractional integral of
standard Brownian motion and of the non-stationary/stationary
Ornstein-Uhlenbeck processes, the covariance functions are carried out in
closed-form. In order to clarify how the fractional order parameter $\alpha$
affects these functions, their numerical evaluations are shown and compared
also with those of the corresponding processes obtained by ordinary Riemann
integral. The results are useful for fractional neuronal models with long range
memory dynamics and involving correlated input processes. The simulation of
these fractional integrated processes can be performed starting from the
obtained covariance functions. A suitable neuronal model is proposed. Graphical
comparisons are provided and discussed.
