Mathematical Modelling of Hereditarity Airy Oscillator with Friction

Abstract

Work is devoted to mathematical modelling hereditarity oscillatory systems with the help of the mathematical apparatus of fractional calculus on the example of an Airy oscillator with friction. Model Airy equation was written in terms of Gerasimov - Caputo fractional derivatives. Next a finite-difference scheme to this generalized equation for numerical computation was proposed. The problems of approximation, stability and convergence of a numerical scheme are considered. The results of simulations are presented based on numerical solutions waveforms and phase trajectories depending on different values of the control parameters are built.