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Czechoslovak Journal of Physics

, Volume 51, Issue 12, pp 1348–1354 | Cite as

Fractional sequential mechanics — models with symmetric fractional derivative

  • Małgorzata Klimek
Article

Abstract

The symmetric fractional derivative is introduced and its properties are studied. The Euler-Lagrange equations for models depending on sequential derivatives of type are derived using minimal action principle. The Hamiltonian for such systems is introduced following methods of classical generalized mechanics and the Hamilton’s equations are obtained. It is explicitly shown that models of fractional sequential mechanics are non-conservative. The limiting procedure recovers classical generalized mechanics of systems depending on higher order derivatives. The method is applied to fractional deformation of harmonic oscillator and to the case of classical frictional force proportional to velocity.

Keywords

Harmonic Oscillator Fractional Derivative Fractional Calculus High Order Derivative Composition Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 2001

Authors and Affiliations

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

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