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

Stochastic dynamics of nonlinear systems with a fractional power-law nonlinear term: The fractional calculus approach,10.1016/j.probengmech.2010.06.01

Stochastic dynamics of nonlinear systems with a fractional power-law nonlinear term: The fractional calculus approach  
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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.
Journal: Probabilistic Engineering Mechanics - PROBABILISTIC ENG MECH , vol. 26, no. 1, pp. 101-108, 2011
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