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On the fractional Kelvin-Voigt oscillator

Vaz Jr, Jayme ; de Oliveira, Edmundo Capelas

Mathematics in Engineering, 2022-01, Vol.4 (1), p.1-23 [Periódico revisado por pares]

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Título:
On the fractional Kelvin-Voigt oscillator
Autor: Vaz Jr, Jayme ; de Oliveira, Edmundo Capelas
Assuntos: caputo fractional derivative ; fractional calculus ; kelvin-voigt oscillator ; mittag-leffler function ; multivariate mittag-leffler function
É parte de: Mathematics in Engineering, 2022-01, Vol.4 (1), p.1-23
Descrição: 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 [alpha] of the fractional derivative (0 < [alpha] [less than or equal to] 1), and compare them with the usual [alpha] = 1 solutions in the underdamped, overdamped and critically damped situations. Keywords: fractional calculus; Kelvin-Voigt oscillator; Caputo fractional derivative; Mittag-Leffler function; multivariate Mittag-Leffler function
Editor: AIMS Press
Idioma: Inglês

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