TY  - JOUR
AU  - Vaz Jr., Jayme
AU  - de Oliveira, Edmundo Capelas
PY  - 2022
TI  - On the fractional Kelvin-Voigt oscillator
JO  - Mathematics in Engineering
SP  - 1
EP  - 23
VL  - 4
IS  - 1
AB  - In this paper we discuss the model of fractional oscillator where the inertial and restoring force terms maintains their usual expression but the damping term involves a fractional derivative of Caputo type, the so called fractional Kelvin-Voigt oscillator. The transient solution of this model is given in terms of the so called bivariate Mittag-Leffler function, while the steady-state solution in response to a sinusoidal force involves a 4-variate Mittag-Leffler function. We give numerical examples comparing the solutions for different values of the order    α of the fractional derivative (   0  <  α  ≤  1), and compare them with the usual    α  =  1 solutions in the underdamped, overdamped and critically damped situations.
UR  - https://doi.org/10.3934/mine.2022006
DO  - 10.3934/mine.2022006