  The fractional order system, which is described by the fractional order
derivative and integral, has been studied in many engineering areas. Recently,
the concept of fractional order has been generalized to the distributed order
concept, which is a parallel connection of fractional order integrals and
derivatives taken to the infinitesimal limit in delta order. On the other hand,
there are very few numerical methods available for the analysis of distributed
order systems, particularly under stochastic forcing. This paper first proposes
a numerical scheme for analyzing the behavior of a SISO linear system with a
single term distributed order differentiator/integrator using an operational
matrix in the time domain under both deterministic and random forcing. To
assess the stochastic distributed order system, the existing Monte-Carlo,
polynomial chaos and frequency methods are first adopted to the stochastic
distributed order system for comparison. The numerical examples demonstrate the
accuracy and computational efficiency of the proposed method for analyzing
stochastic distributed order systems.
