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Lagrangian and Hamiltonian mechanics on fractals subset of real-line. (English) Zbl 1282.70033

Summary: A discontinuous media can be described by fractal dimensions. Fractal objects has special geometric properties, which are discrete and discontinuous structure. A fractal-time diffusion equation is a model for subdiffusive. In this work, we have generalized the Hamiltonian and Lagrangian dynamics on fractal using the fractional local derivative, so one can use as a new mathematical model for the motion in the fractal media. More, Poisson bracket on fractal subset of real line is suggested.

MSC:

70H03 Lagrange’s equations
70H05 Hamilton’s equations
28A80 Fractals
26A33 Fractional derivatives and integrals
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