Stochastic dynamics of nonlinear systems with a fractional power-law nonlinear term: The fractional calculus approach

Fractional power-law nonlinear drift arises in many applications of engineering interest, as in structures with nonlinear fluid viscous-elastic dampers. The probabilistic characterization of such structures under external Gaussian white noise excitation is still an open problem.This paper addresses the solution of such a nonlinear system providing the equation governing the evolution of the characteristic function, which involves the Riesz fractional operator. An efficient numerical procedure to handle the problem is also proposed.