International Journal of Theoretical Physics

, Volume 52, Issue 11, pp 4210–4217 | Cite as

Lagrangian and Hamiltonian Mechanics on Fractals Subset of Real-Line

  • Alireza Khalili Golmankhaneh
  • Ali Khalili Golmankhaneh
  • Dumitru Baleanu
Article

Abstract

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.

Keywords

Fractal calculus Lagrangian mechanics Hamiltonian mechanics Poisson bracket Variational calculus 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Alireza Khalili Golmankhaneh
    • 1
  • Ali Khalili Golmankhaneh
    • 1
  • Dumitru Baleanu
    • 2
    • 3
    • 4
  1. 1.Department of PhysicsIslamic Azad University, Urmia BranchUrmiaIran
  2. 2.Department of Mathematics and Computer ScienceÇankaya UniversityAnkaraTurkey
  3. 3.Institute of Space SciencesMagurele-BucharestRomania
  4. 4.Department of Chemical and Materials Engineering, Faculty of EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia

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