Lagrangian and Hamiltonian Mechanics on Fractals Subset of Real-Line
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- Golmankhaneh, A.K., Golmankhaneh, A.K. & Baleanu, D. Int J Theor Phys (2013) 52: 4210. doi:10.1007/s10773-013-1733-x
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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.