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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.

70H03Lagrange’s equations
70H05Hamilton’s equations
26A33Fractional derivatives and integrals (real functions)
Full Text: DOI
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