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Keywords = Bateman oscillators

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10 pages, 272 KB  
Article
Bateman Oscillators: Caldirola-Kanai and Null Lagrangians and Gauge Functions
by Lesley C. Vestal and Zdzislaw E. Musielak
Physics 2021, 3(2), 449-458; https://doi.org/10.3390/physics3020030 - 12 Jun 2021
Cited by 8 | Viewed by 3328
Abstract
The Lagrange formalism is developed for Bateman oscillators, which includes both damped and amplified systems, and a novel method to derive the Caldirola-Kanai and null Lagrangians is presented. For the null Lagrangians, the corresponding gauge functions are obtained. It is shown that the [...] Read more.
The Lagrange formalism is developed for Bateman oscillators, which includes both damped and amplified systems, and a novel method to derive the Caldirola-Kanai and null Lagrangians is presented. For the null Lagrangians, the corresponding gauge functions are obtained. It is shown that the gauge functions can be used to convert the undriven Bateman oscillators into the driven ones. Applications of the obtained results to quantizatation of the Bateman oscillators are briefly discussed. Full article
(This article belongs to the Section Classical Physics)
13 pages, 1849 KB  
Article
Bateman–Feshbach Tikochinsky and Caldirola–Kanai Oscillators with New Fractional Differentiation
by Antonio Coronel-Escamilla, José Francisco Gómez-Aguilar, Dumitru Baleanu, Teodoro Córdova-Fraga, Ricardo Fabricio Escobar-Jiménez, Victor H. Olivares-Peregrino and Maysaa Mohamed Al Qurashi
Entropy 2017, 19(2), 55; https://doi.org/10.3390/e19020055 - 28 Jan 2017
Cited by 60 | Viewed by 5798
Abstract
In this work, the study of the fractional behavior of the Bateman–Feshbach–Tikochinsky and Caldirola–Kanai oscillators by using different fractional derivatives is presented. We obtained the Euler–Lagrange and the Hamiltonian formalisms in order to represent the dynamic models based on the Liouville–Caputo, Caputo–Fabrizio–Caputo and [...] Read more.
In this work, the study of the fractional behavior of the Bateman–Feshbach–Tikochinsky and Caldirola–Kanai oscillators by using different fractional derivatives is presented. We obtained the Euler–Lagrange and the Hamiltonian formalisms in order to represent the dynamic models based on the Liouville–Caputo, Caputo–Fabrizio–Caputo and the new fractional derivative based on the Mittag–Leffler kernel with arbitrary order α. Simulation results are presented in order to show the fractional behavior of the oscillators, and the classical behavior is recovered when α is equal to 1. Full article
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory II)
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