  In this paper we consider fractional higher-order stochastic differential
equations of the form \begin{align*} \left( \mu + c_\alpha
\frac{d^\alpha}{d(-t)^\alpha} \right)^\beta X(t) = \mathcal{E}(t) , \quad t\geq
0,\; \mu>0,\; \beta>0,\; \alpha \in (0,1) \cup \mathbb{N} \end{align*} where
$\mathcal{E}(t)$ is a Gaussian white noise. We derive stochastic processes
satisfying the above equations of which we obtain explicitly the covariance
functions and the spectral functions.

Probability