Bateman–Feshbach Tikochinsky and Caldirola–Kanai Oscillators with New Fractional Differentiation

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...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2017-02, Vol.19 (2), p.55-55
Main Authors: Coronel-Escamilla, Antonio, Gómez-Aguilar, José, Baleanu, Dumitru, Córdova-Fraga, Teodoro, Escobar-Jiménez, Ricardo, Olivares-Peregrino, Victor, Qurashi, Maysaa
Format: Article
Language:English
Subjects:
Computer simulation
Derivatives
Differentiation
Dynamic models
Entropy
Formalism
Kernels
Oscillators
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Summary: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.
ISSN:1099-4300
1099-4300
DOI:10.3390/e19020055