A method is presented to compute the stochastic response of single-degree-of-freedom (SDOF) structural
systems with fractional derivative damping, subjected to stationary and non-stationary inputs. Based on
a few manipulations involving an appropriate change of variable and a discretization of the fractional
derivative operator, the equation of motion is reverted to a set of coupled linear equations involving
additional degrees of freedom, the number of which depends on the discretization of the fractional
derivative operator. As a result of the proposed variable transformation and discretization, the stochastic
analysis becomes very straightforward and simple since, based on standard rules of stochastic calculus,
it is possible to handle a system featuring Markov response processes of first order and not of infinite
order like the original one. Specifically, for inputs of most relevant engineering interest, it is seen that
the response second-order statistics can be readily obtained in a closed form, to be implemented in any
symbolic package. The method applies for fractional damping of arbitrary order α (0 ≤ α ≤ 1). The
results are compared to Monte Carlo simulation data
