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 role, 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 fractionally integrated processes can be performed starting from the obtained covariance functions. A suitable neuronal model is proposed. Graphical comparisons are provided and discussed.

我们调查随机过程作为分数阶黎曼-李维尔积分 $\alpha \in （0，\mathrm{1个}）$高斯-马尔可夫过程。给出了均值，方差和协方差函数的一般表达式。由于中心作用，对于标准布朗运动和非平稳/平稳Ornstein-Uhlenbeck过程的分数积分，协方差函数以封闭形式执行。为了阐明分数阶参数如何$\alpha$影响这些函数，将显示它们的数值评估，并将其与通过普通Riemann积分获得的相应过程的数值评估进行比较。该结果对于具有长距离记忆动力学并涉及相关输入过程的分数神经元模型很有用。这些分数积分过程的仿真可以从获得的协方差函数开始进行。提出了合适的神经元模型。提供了图形比较并进行了讨论。