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Browsing by Author "Gasimov, Yusif S."

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    Classical Mechanics on Fractal Curves
    (Springer Heidelberg, 2023) Golmankhaneh, Alireza Khalili; Welch, Kerri; Tunc, Cemil; Gasimov, Yusif S.
    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.