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Control of damping oscillations by fractional differential operator with time-dependent order. (English) Zbl 1079.70020
Summary: The aim is an application of a differential operator of variable order to constitutive relations for viscoelastic materials. This operator is used for studying the vibrations of a one-degree-of-freedom oscillator in which the viscoelastic deformation is governed by a servo-order function. A method for numerical determination of the eigenfrequency of the fractional differential equation is proposed.

70Q05Control of mechanical systems (general mechanics)
70J35Forced linear oscillatory motions
93C15Control systems governed by ODE
74D05Linear constitutive equations (materials with memory)
Full Text: DOI
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