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Fractional Hamiltonian of Nonconservative Systems with Second Order Lagrangian

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), 2018. 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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[10] O. P. Agrawal, An Analytical Scheme for Stochastic Dynamics Systems Containing Fractional Derivatives. ASME Design Engineering Technical Conferences. (1999).
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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

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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
  • Applied Physics Department, Faculty of Science, Tafila Technical University, Tafila, Jordan

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

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