an:05687098
Zbl 1183.70062
Huang, Z. L.; Jin, X. L.; Lim, C. W.; Wang, Y.
Statistical analysis for stochastic systems including fractional derivatives
EN
Nonlinear Dyn. 59, No. 1-2, 339-349 (2010).
00257377
2010
j
70L05 26A33
statistical behavior; fractional derivatives; Laplace transform; Duhamel integral; numerical simulation
Summary: An analytical scheme to determine the statistical behavior of a stochastic system including two terms of fractional derivative with real, arbitrary, fractional orders is proposed. In this approach, Green's functions obtained are based on a Laplace transform approach and the weighted generalized Mittag-Leffler function. The responses of the system can be subsequently described as a Duhamel integral-type close-form expression. These expressions are applied to obtain the statistical behavior of a dynamical system excited by stationary stochastic processes. The numerical simulation based on the modified Euler method and Monte Carlo approach is developed. Three examples of single-degree-of-freedom system with fractional derivative damping under Gaussian white noise excitation are presented to illustrate application of the proposed method.