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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:
70H03Lagrange’s equations
70H05Hamilton’s equations
28A80Fractals
26A33Fractional derivatives and integrals (real functions)
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References:
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