Czechoslovak Journal of Physics

, Volume 52, Issue 11, pp 1247–1253 | Cite as

Lagrangean and Hamiltonian fractional sequential mechanics

  • Małgorzata Klimek


The models described by fractional order derivatives of Riemann-Liouville type in sequential form are discussed in Lagrangean and Hamiltonian formalism. The Euler-Lagrange equations are derived using the minimum action principle. Then the methods of generalized mechanics are applied to obtain the Hamilton’s equations. As an example free motion in fractional picture is studied. The respective fractional differential equations are explicitly solved and it is shown that the limitα→1+ recovers classical model with linear trajectories and constant velocity.


03.20.+i 46.10.+z 02.30.-f 46.90.+s 

Key words

fractional derivative fractional integral fractional mechanics Euler-Lagrange equations Hamilton equation non-conservative systems 


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Copyright information

© Springer 2002

Authors and Affiliations

  • Małgorzata Klimek
    • 1
  1. 1.Institute of Mathematics and Computer ScienceTechnical University of CzęstochowaCzęstochowaPoland

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