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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.

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