Classical mechanics on fractal curves
Artificial Intelligence and Big Data Automation Research Center, Urmia Branch, Islamic Azad University, Urmia, Iran
2 Faculty at California Institute of Integral Studies, 94103, San Francisco, CA, USA
3 Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080-Campus, Van, Turkey
4 Azerbaijan University, Jeyhun Hajibeyli Str., 71, AZ1007, Baku, Azerbaijan
5 Institute of Mathematics and Mechanics, B. Vahabzade Str., 9, AZ1148, Baku, Azerbaijan
6 Institute for Physical Problems, Baku State University, Z. Khalilov Str., 23, AZ1148, Baku, Azerbaijan
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Accepted: 24 January 2023
Published online: 17 February 2023
Fractal analogue of Newton, Lagrange, Hamilton, and Appell’s mechanics are suggested. The fractal -velocity and -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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