Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian

Ola Jarab'ah; Khaled Nawafleh

doi:doi:10.11648/j.ajpa.20180604.12

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Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian

Ola Jarab'ah, Khaled Nawafleh

Published in American Journal of Physics and Applications (Volume 6, Issue 4)

Received: 5 July 2018 Accepted: 19 July 2018 Published: 24 August 2018

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Abstract

In this paper, the nonconservative systems with second order Lagrangian are investigated using fractional derivatives. The fractional Euler Lagrange equations for these systems are obtained. Then, fractional Hamiltonian for these systems is constructed, which is used to find the Hamilton's equations of motion in the same manner as those obtained by using the formulation of Euler Lagrange equations from variational problems, and it is observed that the Hamiltonian formulation is in exact agreement with the Lagrangian formulation. The passage from the Lagrangian containing fractional derivatives to the Hamiltonian is achieved. We have examined one example to illustrate the formalism.

Published in	American Journal of Physics and Applications (Volume 6, Issue 4)
DOI	10.11648/j.ajpa.20180604.12
Page(s)	85-88
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Fractional Derivatives, Lagrangian Formulation, Hamiltonian Formulation, Nonconservative Systems, Euler Lagrange Equations, Second Order Lagrangian

References

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[9]	E. M. Rabei, K. I. Nawafleh, R. S. Hijjawi, S. I. Muslih, and D. Baleanu, Journal of Mathematical Analysis and Applications 327, 891 (2007).
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Ola Jarab'ah, Khaled Nawafleh. (2018). Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian. American Journal of Physics and Applications, 6(4), 85-88. https://doi.org/10.11648/j.ajpa.20180604.12

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ACS Style

Ola Jarab'ah; Khaled Nawafleh. Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian. Am. J. Phys. Appl. 2018, 6(4), 85-88. doi: 10.11648/j.ajpa.20180604.12

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AMA Style

Ola Jarab'ah, Khaled Nawafleh. Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian. Am J Phys Appl. 2018;6(4):85-88. doi: 10.11648/j.ajpa.20180604.12

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@article{10.11648/j.ajpa.20180604.12,
  author = {Ola Jarab'ah and Khaled Nawafleh},
  title = {Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian},
  journal = {American Journal of Physics and Applications},
  volume = {6},
  number = {4},
  pages = {85-88},
  doi = {10.11648/j.ajpa.20180604.12},
  url = {https://doi.org/10.11648/j.ajpa.20180604.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20180604.12},
  abstract = {In this paper, the nonconservative systems with second order Lagrangian are investigated using fractional derivatives. The fractional Euler Lagrange equations for these systems are obtained. Then, fractional Hamiltonian for these systems is constructed, which is used to find the Hamilton's equations of motion in the same manner as those obtained by using the formulation of Euler Lagrange equations from variational problems, and it is observed that the Hamiltonian formulation is in exact agreement with the Lagrangian formulation. The passage from the Lagrangian containing fractional derivatives to the Hamiltonian is achieved. We have examined one example to illustrate the formalism.},
 year = {2018}
}

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TY  - JOUR
T1  - Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian
AU  - Ola Jarab'ah
AU  - Khaled Nawafleh
Y1  - 2018/08/24
PY  - 2018
N1  - https://doi.org/10.11648/j.ajpa.20180604.12
DO  - 10.11648/j.ajpa.20180604.12
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 85
EP  - 88
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20180604.12
AB  - In this paper, the nonconservative systems with second order Lagrangian are investigated using fractional derivatives. The fractional Euler Lagrange equations for these systems are obtained. Then, fractional Hamiltonian for these systems is constructed, which is used to find the Hamilton's equations of motion in the same manner as those obtained by using the formulation of Euler Lagrange equations from variational problems, and it is observed that the Hamiltonian formulation is in exact agreement with the Lagrangian formulation. The passage from the Lagrangian containing fractional derivatives to the Hamiltonian is achieved. We have examined one example to illustrate the formalism.
VL  - 6
IS  - 4
ER  -

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Author Information

Ola Jarab'ah

Applied Physics Department, Faculty of Science, Tafila Technical University, Tafila, Jordan
Khaled Nawafleh

Department of Physics, Faculty of Science, Mu'tah University, AL-Karak, Jordan

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APA Style

Ola Jarab'ah, Khaled Nawafleh. (2018). Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian. American Journal of Physics and Applications, 6(4), 85-88. https://doi.org/10.11648/j.ajpa.20180604.12

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ACS Style

Ola Jarab'ah; Khaled Nawafleh. Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian. Am. J. Phys. Appl. 2018, 6(4), 85-88. doi: 10.11648/j.ajpa.20180604.12

Copy | Download

AMA Style

Ola Jarab'ah, Khaled Nawafleh. Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian. Am J Phys Appl. 2018;6(4):85-88. doi: 10.11648/j.ajpa.20180604.12

Copy | Download

@article{10.11648/j.ajpa.20180604.12,
  author = {Ola Jarab'ah and Khaled Nawafleh},
  title = {Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian},
  journal = {American Journal of Physics and Applications},
  volume = {6},
  number = {4},
  pages = {85-88},
  doi = {10.11648/j.ajpa.20180604.12},
  url = {https://doi.org/10.11648/j.ajpa.20180604.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20180604.12},
  abstract = {In this paper, the nonconservative systems with second order Lagrangian are investigated using fractional derivatives. The fractional Euler Lagrange equations for these systems are obtained. Then, fractional Hamiltonian for these systems is constructed, which is used to find the Hamilton's equations of motion in the same manner as those obtained by using the formulation of Euler Lagrange equations from variational problems, and it is observed that the Hamiltonian formulation is in exact agreement with the Lagrangian formulation. The passage from the Lagrangian containing fractional derivatives to the Hamiltonian is achieved. We have examined one example to illustrate the formalism.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian
AU  - Ola Jarab'ah
AU  - Khaled Nawafleh
Y1  - 2018/08/24
PY  - 2018
N1  - https://doi.org/10.11648/j.ajpa.20180604.12
DO  - 10.11648/j.ajpa.20180604.12
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 85
EP  - 88
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20180604.12
AB  - In this paper, the nonconservative systems with second order Lagrangian are investigated using fractional derivatives. The fractional Euler Lagrange equations for these systems are obtained. Then, fractional Hamiltonian for these systems is constructed, which is used to find the Hamilton's equations of motion in the same manner as those obtained by using the formulation of Euler Lagrange equations from variational problems, and it is observed that the Hamiltonian formulation is in exact agreement with the Lagrangian formulation. The passage from the Lagrangian containing fractional derivatives to the Hamiltonian is achieved. We have examined one example to illustrate the formalism.
VL  - 6
IS  - 4
ER  -

Copy | Download