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Open AccessArticle

Fractional Mass-Spring-Damper System Described by Generalized Fractional Order Derivatives

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Laboratoire Lmdan, Département de Mathématiques de la Décision, Université Cheikh Anta Diop de Dakar, Faculté des Sciences Economiques et Gestion, BP 5683 Dakar Fann, Senegal
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CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Morelos, Mexico
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Author to whom correspondence should be addressed.
Fractal Fract 2019, 3(3), 39; https://doi.org/10.3390/fractalfract3030039
Received: 21 May 2019 / Revised: 4 July 2019 / Accepted: 5 July 2019 / Published: 7 July 2019
This paper proposes novel analytical solutions of the mass-spring-damper systems described by certain generalized fractional derivatives. The Liouville–Caputo left generalized fractional derivative and the left generalized fractional derivative were used. The behaviors of the analytical solutions of the mass-spring-damper systems described by the left generalized fractional derivative and the Liouville–Caputo left generalized fractional derivative were represented graphically and the effect of the orders of the fractional derivatives analyzed. We finish by analyzing the global asymptotic stability and the converging-input-converging-state of the unforced mass-damper system, the unforced spring-damper, the spring-damper system, and the mass-damper system. View Full-Text
Keywords: mass-spring-damper systems; Liouville–Caputo generalized fractional derivative; left generalized fractional derivative; global asymptotic stability mass-spring-damper systems; Liouville–Caputo generalized fractional derivative; left generalized fractional derivative; global asymptotic stability
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Sene, N.; Gómez Aguilar, J.F. Fractional Mass-Spring-Damper System Described by Generalized Fractional Order Derivatives. Fractal Fract 2019, 3, 39.

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