International Journal of Theoretical Physics

, Volume 52, Issue 11, pp 4210–4217

Lagrangian and Hamiltonian Mechanics on Fractals Subset of Real-Line


  • Alireza Khalili Golmankhaneh
    • Department of PhysicsIslamic Azad University, Urmia Branch
  • Ali Khalili Golmankhaneh
    • Department of PhysicsIslamic Azad University, Urmia Branch
    • Department of Mathematics and Computer ScienceÇankaya University
    • Institute of Space Sciences
    • Department of Chemical and Materials Engineering, Faculty of EngineeringKing Abdulaziz University

DOI: 10.1007/s10773-013-1733-x

Cite this article as:
Golmankhaneh, A.K., Golmankhaneh, A.K. & Baleanu, D. Int J Theor Phys (2013) 52: 4210. doi:10.1007/s10773-013-1733-x


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.


Fractal calculusLagrangian mechanicsHamiltonian mechanicsPoisson bracketVariational calculus

Copyright information

© Springer Science+Business Media New York 2013