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Lagrangian and Hamiltonian Mechanics on Fractals Subset of Real-Line

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Abstract

A discontinuous media can be described by fractal dimensions. Fractal objects has special geometric properties, which are discrete and discontinuous structure. A fractal-time diffusion equation is a model for subdiffusive. In this work, we have generalized the Hamiltonian and Lagrangian dynamics on fractal using the fractional local derivative, so one can use as a new mathematical model for the motion in the fractal media. More, Poisson bracket on fractal subset of real line is suggested.

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Authors and Affiliations

  1. Department of Physics, Islamic Azad University, Urmia Branch, PO Box 969, Urmia, Iran

    Alireza Khalili Golmankhaneh & Ali Khalili Golmankhaneh

  2. Department of Mathematics and Computer Science, Çankaya University, 06530, Ankara, Turkey

    Dumitru Baleanu

  3. Institute of Space Sciences, P.O. BOX, MG-23, R76900, Magurele-Bucharest, Romania

    Dumitru Baleanu

  4. Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, 21589, Saudi Arabia

    Dumitru Baleanu

Authors
  1. Alireza Khalili Golmankhaneh
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  2. Ali Khalili Golmankhaneh
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  3. Dumitru Baleanu
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Correspondence to Dumitru Baleanu.

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Golmankhaneh, A.K., Golmankhaneh, A.K. & Baleanu, D. Lagrangian and Hamiltonian Mechanics on Fractals Subset of Real-Line. Int J Theor Phys 52, 4210–4217 (2013). https://doi.org/10.1007/s10773-013-1733-x

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  • DOI: https://doi.org/10.1007/s10773-013-1733-x

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