Based on operational matrix technique,explicit relations between first and second order moments of stochastic input and output for linear fractional order system are derived.
Ref.:
[1] Pham Luu Trung Duong & Moonyong Lee
,Uncertainty quantification for fractional order PI control system: polynomial chaos approach IFAC
conference on PID control 2012 Brescia, Italy,
[2] Pham Luu Trung Duong & Moonyong Lee
,Uncertainty propagation in stochastic fractional order processes using spectral methods(Commun Nonlinear Sci Numer Simulat 2012) doi:10.1016/j.cnsns.2012.01.031
http://www.sciencedirect.com/science/article/pii/S1007570412000536
[3]M . Grigoriu Linear systems with fractional Brownian motion and Gaussian noise Probabilistic Engineering Mechanics 22 (2007) 276–284
[4]Pham Luu Trung Duong & Moonyong Lee, Deterministic and stochastic analysis of distributed order systems using operational matrix, http://arxiv.org/abs/1312.3048