Bateman-Feshbach Tikochinsky and Caldirola-Kanai Oscillators with New Fractional Differentiation
Date
2017
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Publisher
MDPI
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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 the new fractional derivative based on the Mittag-Leffler kernel with arbitrary order . Simulation results are presented in order to show the fractional behavior of the oscillators, and the classical behavior is recovered when is equal to 1.
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Keywords
Bateman-Feshbach Tikochinsky Oscillator, Caldirola-Kanai Oscillator, Fractional Operators, Mittag-Leffler Kernel
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Citation
Coronel-Escamilla, Antonio...et al. (2017). Bateman-Feshbach Tikochinsky and Caldirola-Kanai Oscillators with New Fractional Differentiation, Entropy, 19(2).
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Source
Entropy
Volume
19
Issue
2