Can we refer to Hamilton’s equations for an oscillator with friction?

Shalashov, A. G.

doi:10.3367/ufne.2017.12.038273

Cited by 5 publications

(2 citation statements)

References 24 publications

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“…The principle of least action is often used to describe dissipative systems, in particular in the case of linear oscillators with viscous friction [26]. In this paper, we used this principle in the context of fractional calculus.…”

Section: Discussionmentioning

confidence: 99%

Ordinary Differential Equation with Left and Right Fractional Derivatives and Modeling of Oscillatory Systems

2020

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We consider the principle of least action in the context of fractional calculus. Namely, we derive the fractional Euler–Lagrange equation and the general equation of motion with the composition of the left and right fractional derivatives defined on infinite intervals. In addition, we construct an explicit representation of solutions to a model fractional oscillator equation containing the left and right Gerasimov–Caputo fractional derivatives with origins at plus and minus infinity. We derive a representation for the composition of the left and right derivatives with origins at plus and minus infinity in terms of the Riesz potential, and introduce special functions with which we give solutions to the model fractional oscillator equation with a complex coefficient. This approach can be useful for describing dissipative dynamical systems with the property of heredity.

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Section: Discussionmentioning

confidence: 99%

Ordinary Differential Equation with Left and Right Fractional Derivatives and Modeling of Oscillatory Systems

2020

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“…However, Riffe failed to obtain a rigorous solution to the classical problem; in particular, normal oscillations of a coupled system of oscillators have not been found. It should be noted that the Fano problem was formulated in quantum mechanics for a conservative system, while in the classical analog [18] a fundamental role is played by the damping of oscillators, due to which the time reversal symmetry is violated and equations of motion become nonconservative [22].…”

Section: History Of the Issue And Description Of The Fano Problemmentioning

confidence: 99%