On fractional forced oscillator

Fractional calculus is widely used in formulation of constitutive relations for viscoelastic materials. Problems of vibration of continuous structures, when such constitutive relations are used, leads to fractional differential equations similar to the equation of forced, damped, harmonic oscillator. In this paper two fractional oscillators are investigated (corresponding to two constitutive relations of viscoelastic materials). Closed-form solutions are obtained using Laplace Transform method, resonance curves for these oscillators are calculated numerically, and influence on its shape of the model parameters are analyzed.