@article{Vaz Jr.2022, 
author = {Jayme Vaz Jr. and Edmundo Capelas de Oliveira},
title = {On the fractional Kelvin-Voigt oscillator},
year = {2022},
journal = {Mathematics in Engineering},
volume = {4},
number = {1},
pages = {1-23},
keywords = {fractional calculus, Kelvin-Voigt oscillator, Caputo fractional derivative, Mittag-Leffler function, multivariate Mittag-Leffler function},
url = {https://www.sciopen.com/article/10.3934/mine.2022006},
doi = {10.3934/mine.2022006},
abstract = {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.}
}