International Journal of Theoretical Physics

, Volume 49, Issue 2, pp 293–303 | Cite as

Fractional Dynamics of Relativistic Particle

  • Vasily E. Tarasov


Fractional dynamics of relativistic particle is discussed. Derivatives of fractional orders with respect to proper time describe long-term memory effects that correspond to intrinsic dissipative processes. Relativistic particle subjected to a non-potential four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u μ u μ +c 2=0, where c is a speed of light in vacuum. In the general case, the fractional dynamics of relativistic particle is described as non-Hamiltonian and dissipative. Conditions for fractional relativistic particle to be a Hamiltonian system are considered.

Fractional derivative Fractional dynamics Relativistic dynamics Relativistic particle Nonholonomic constraints Dissipation 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Skobeltsyn Institute of Nuclear PhysicsMoscow State UniversityMoscowRussia

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