Golmankhaneh, Alireza KhaliliWelch, KerriTunc, CemilGasimov, Yusif S.2025-05-102025-05-1020231951-63551951-640110.1140/epjs/s11734-023-00775-y2-s2.0-85148351461https://doi.org/10.1140/epjs/s11734-023-00775-yhttps://hdl.handle.net/20.500.14720/1053Khalili Golmankhaneh, Alireza/0000-0002-5008-0163Fractal 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.eninfo:eu-repo/semantics/closedAccessArticle2327Q2Q2991999WOS:000936170600002