Numerical Study for Fractional Euler-Lagrange Equations of a Harmonic Oscillator on a Moving Platform

Băleanu, Dumitru; Błaszczyk, Tomasz; Asad, Jihad; Alipour, Mohsen

doi:10.12693/aphyspola.130.688

Cited by 9 publications

(8 citation statements)

References 26 publications

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“…We found an oscillatory behaviour of the above thermodynamic properties modulated by quantum size effects. Similar oscillations can also be observed in other physical systems [12][13][14][15][16]. Moreover, we proved that the thermodynamic properties of Pb films cannot be correctly described using the BCS theory of superconductivity due to the strong coupling and retardation effects.…”

Section: Introductionsupporting

confidence: 78%

On the Magnetic Penetration Depth in Superconducting Ultrathin Lead Films

Durajski

Szczȩśniak

2017

Acta Phys. Pol. A

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In the present paper, we report a theoretical study of the magnetic London penetration depth in ultrathin Pb films consisting of five to ten monolayers. Our calculations were performed within the framework of the strongcoupling approach. We observed that for thin films, the thermodynamic parameter exhibits an oscillatory behaviour connected with a quantum size effect. Moreover, we proved that the London penetration depth of Pb films cannot be correctly described using the Bardeen-Cooper-Schrieffer theory of superconductivity due to the strong-coupling and retardation effects. The Eliashberg theory, used in this paper, goes beyond the BCS theory to include these effects which allows to describe the superconducting state on the quantitative level.

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Section: Introductionsupporting

confidence: 78%

On the Magnetic Penetration Depth in Superconducting Ultrathin Lead Films

Durajski

Szczȩśniak

2017

Acta Phys. Pol. A

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“…Like many other complex systems [28][29][30][31][32][33], the Eliashberg equations are too complicated to solve them in an analytical way. Due to the above, in this study the numerical analysis was performed using a self-consistent iteration methods [34], which were implemented successfully in our previous papers [35][36][37][38].…”

Section: Theoretical Model and Computational Methodsmentioning

confidence: 99%

Non-Adiabatic Effects in Superconducting Intermetallic Borocarbides

2019

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In this work, we systematically study the non-adiabatic effects on the superconductivity of selected intermetallic borocarbides. Using the strong-coupling Eliashberg theory with and without lowest-order vertex correction we find that for a fixed experimental value of critical temperature the Coulomb pseudopotential can take different values, however, the superconducting order parameter remains practically unaffected. From the physical point of view, it means that in the investigated superconductors the lowest-order vertex correction does not play a significant role.

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“…For more details on the fractional derivatives and their properties, the readers can refer to [1][2][3].…”

Section: Preliminariesmentioning

confidence: 99%

“…It has been demonstrated that the fractional order representation provides a more realistic behavior of complex systems appearing in various fields of science and engineering [3]. Due to this fact, fractional calculus has some applications in chemistry [4], bioengineering [5], hydrologic modelling [6], pharmacokinetics [7], heat transfer modelling [8], viscoelasticity [9], etc.…”

Section: Introductionmentioning

confidence: 99%

The Motion of a Bead Sliding on a Wire in Fractional Sense

et al. 2017

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In this study, we consider the motion of a bead sliding on a wire which is bent into a parabola form. We first introduce the classical Lagrangian from the system model under consideration and obtain the classical EulerLagrange equation of motion. As the second step, we generalize the classical Lagrangian to the fractional form and derive the fractional Euler-Lagrange equation in terms of the Caputo fractional derivatives. Finally, we provide numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on a discretization scheme using a Grünwald-Letnikov approximation for the fractional derivatives. Numerical simulations verify that the proposed approach is efficient and easy to implement.

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Numerical Study for Fractional Euler-Lagrange Equations of a Harmonic Oscillator on a Moving Platform

Cited by 9 publications

References 26 publications

On the Magnetic Penetration Depth in Superconducting Ultrathin Lead Films

On the Magnetic Penetration Depth in Superconducting Ultrathin Lead Films

Non-Adiabatic Effects in Superconducting Intermetallic Borocarbides

The Motion of a Bead Sliding on a Wire in Fractional Sense

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