Fractional differential equations under stochastic input processes handled by the improved pseudo-force approach

This paper presents a step-by-step procedure for the numerical integration of the fractional differential equation governing the response of a single-degree-of-freedom (SDOF) system with fractional derivative damping. The procedure is developed by extending the improved pseudo-force method proposed by the second author for the numerical integration of classical differential equations. To this aim, the Grünwald–Letnikov approximation of the fractional derivative is adopted. The proposed numerical procedure is exploited to compute response statistics of a SDOF system subjected to stochastic excitation by applying classical Monte Carlo Simulation.