Control of damping oscillations by fractional differential operator with time-dependent order

The aim of the present paper is application of a differential operator of variable order in 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.