Extension of the moment equations method for the systems with fractional derivatives of a wide range of differential order under non-white random excitation

Abstract

In recent years, random response analysis of a system modeled by fractional derivatives has attracted attention. On the other hand, due to the complexity of the mathematical handling of fractional derivatives, in most cases, analysis has been conducted assuming that the input to the system is white noise. In the previous study, as the moment equation method is effective and useful in random response analysis of an integer-order-derivative system, the method was extended. The moment equations corresponding to the system with fractional-order derivative of order 1/2 was derived and the effectiveness to systems under non-white random excitation was verified. In this paper, we extend the method of moment equation proposed in the previous study to a system with fractional derivatives of a wide range of order. Then, we discuss the class of order in which the proposed method can be directly applied or not . Futhermore, for the latter case, we will propose a solution to make it possible to apply the proposed method. Finally, the effectiveness of the method is demonstrated.