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European Physical Journal: Special Topics, vol.232, no.7, pp.991-999, 2023 (SCI-Expanded)
Fractal analogue of Newton, Lagrange, Hamilton, and Appell’s mechanics are suggested. The fractal α-velocity and α-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.