Iteration method for equation of viscoelastic motion with fractional differential operator of damping Original Research Article

Mechanical properties of viscoelastic materials depend on the loading conditions and their history. The work is devoted to the analysis of oscillation processes in viscoelastic media, with loading prehistory taken into account by means of fractional derivative terms in the governing equations. The paper suggests convergent procedure for numerical solution of this type of differential equations and their system for any combination of damping operator orders. The order of the fractional derivative may be as constant, so variable. Analysis of the amplitude–frequency behavior of the oscillator versus the damping operator order is provided.