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Classical mechanics on fractal curves

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Abstract

Fractal analogue of Newton, Lagrange, Hamilton, and Appell’s mechanics are suggested. The fractal \(\alpha\)-velocity and \(\alpha\)-acceleration are defined in order to obtain the Langevin equation on fractal curves. Using the Legendre transformation, Hamilton’s mechanics on fractal curves is derived for modeling a non-conservative system on fractal curves with fractional dimensions. Fractal differential equations have solutions that are non-differentiable in the sense of ordinary derivatives and explain space and time with fractional dimensions. The illustrated examples with graphs present the details.

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Author information

Authors and Affiliations

  1. Artificial Intelligence and Big Data Automation Research Center, Urmia Branch, Islamic Azad University, Urmia, Iran

    Alireza Khalili Golmankhaneh

  2. Faculty at California Institute of Integral Studies, San Francisco, CA, 94103, USA

    Kerri Welch

  3. Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080-Campus, Van, Turkey

    Cemil Tunç

  4. Azerbaijan University, Jeyhun Hajibeyli Str., 71, AZ1007, Baku, Azerbaijan

    Yusif S. Gasimov

  5. Institute of Mathematics and Mechanics, B. Vahabzade Str., 9, AZ1148, Baku, Azerbaijan

    Yusif S. Gasimov

  6. Institute for Physical Problems, Baku State University, Z. Khalilov Str., 23, AZ1148, Baku, Azerbaijan

    Yusif S. Gasimov

Authors
  1. Alireza Khalili Golmankhaneh
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  2. Kerri Welch
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  3. Cemil Tunç
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  4. Yusif S. Gasimov
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Corresponding author

Correspondence to Alireza Khalili Golmankhaneh.

Additional information

S.I. : Framework of Fractals in Data Analysis: Theory and Interpretation. Guest editors: Santo Banerjee, A. Gowrisankar.

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Golmankhaneh, A.K., Welch, K., Tunç, C. et al. Classical mechanics on fractal curves. Eur. Phys. J. Spec. Top. 232, 991–999 (2023). https://doi.org/10.1140/epjs/s11734-023-00775-y

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