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Fractional Hamilton’s equations of motion in fractional time

100%
Muslih S., Baleanu D., Rabei E.
|
EN
The Hamiltonian formulation for mechanical systems containing Riemman-Liouville fractional derivatives are investigated in fractional time. The fractional Hamilton’s equations are obtained and two examples are investigated in detail.
2
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The fractional oscillator as an open system

100%
Tarasov V.
Open Physics
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2012
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vol. 10
|
issue 2
382-389
EN
A dynamical system governed by equations with derivatives of non-integer order, such as the fractional oscillator, can be considered as an open (non-isolated) system with memory. Fractional equations of motion are obtained from the interaction between the system and the environment with power-law spectral density.
3
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Fractional Newtonian mechanics

88%
Baleanu D., Golmankhaneh A., Nigmatullin R., Golmankhaneh A.
Open Physics
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2010
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vol. 8
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issue 1
120-125
EN
In the present paper, we have introduced the generalized Newtonian law and fractional Langevin equation. We have derived potentials corresponding to different kinds of forces involving both the right and the left fractional derivatives. Illustrative examples have worked out to explain the formalism.
4
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Lattice model with power-law spatial dispersion for fractional elasticity

88%
Tarasov V.
Open Physics
|
2013
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vol. 11
|
issue 11
1580-1588
EN
A lattice model with a spatial dispersion corresponding to a power-law type is suggested. This model serves as a microscopic model for elastic continuum with power-law non-locality. We prove that the continuous limit maps of the equations for the lattice with the power-law spatial dispersion into the continuum equations with fractional generalizations of the Laplacian operators. The suggested continuum equations, which are obtained from the lattice model, are fractional generalizations of the integral and gradient elasticity models. These equations of fractional elasticity are solved for two special static cases: fractional integral elasticity and fractional gradient elasticity.
5
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Optimal control problems with a fixed terminal time in linear fractional-order systems

75%
Gomoyunov M. I., Gomoyunov M. I.
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2020
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vol. 30
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issue 4
6
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Fractional Derivatives for Description of Sorption Kinetics in the Plant Sorbent - Metal Ions System

63%
Tomczak E., Kamiński W., Szczerkowska D.
Ecological Chemistry and Engineering S
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2013
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vol. 20
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issue 3
499-506
EN
It was examined if buckwheat hull has a potential to be used to adsorb heavy metal ions Zn(II), Cd(II), Co(II), Cu(II), Ni(II) from water. The research involved experiments aimed at the determination of sorption kinetics taking into consideration changes of concentration in a solution and sorbent over time. According to the literature data, kinetics is described with the use of pseudo first-order equations. Application of fractional derivatives for the description of sorption kinetics enables the development of the generalised sorption kinetics equation. Result analysis with this concept requires making a computational procedure using gamma functions and infinite series. Kinetics description using fractional derivatives will be equations with two parameters ie fraction of derivative α and the kinetics constant K dependent on the analysed sorbent-adsorbate system.
PL
W pracy wykorzystano łuskę gryki do procesu sorpcji jonów metali ciężkich Cu(II), Ni(II), Zn(II), Co(II) i Cd(II) z roztworów wodnych. Wyznaczone zostały maksymalne pojemności sorpcyjne oraz stałe kinetyczne i równowagowe. Obliczone wartości pozwoliły na zastosowanie równań różniczkowych ułamkowych do opisu kinetyki sorpcji oraz uzyskania uogólnionego równania kinetyki sorpcji. Opracowanie wyników według tej koncepcji wymaga napisania procedury obliczeniowej wykorzystującej funkcje gamma oraz szeregi nieskończone. Równania kinetyki z wykorzystaniem pochodnych ułamkowych są równaniami o dwóch parametrach. Są to ułamek pochodnej i stała kinetyczna zależne od analizowanego układu sorbent - adsorbat.
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