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.
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References
K.B. Oldham and J. Spanier:The Fractional Calculus. Academic Press, New York, 1974.
K.S. Miller and B. Ross:An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley and Sons, New York, 1993.
S.G. Samko, A.A. Kilbas, and O.I. Marichev:Fractional Derivatives and Integrals. Theory and Applications. Gordon and Breach, Amsterdam, 1993.
E.R. Love and L.C. Young: Proc. Lond. Math. Soc.44 (1938) 1.
F. Riewe: Phys. Rev. E53 (1996) 1890;55 (1997) 3581.
M. De Leon and P.R. RodriguesGeneralized Classical Mechanics and Field Theory: A Geometrical Approach of Lagrangian and Hamiltonian Formalisms Involving Higher Order Derivatives. North-Holland, Amsterdam, 1985.
B.S. Rubin: Izv. Vyssh. Uchebn. Zaved. Mat.6 (1973) 73.
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Klimek, M. Fractional sequential mechanics — models with symmetric fractional derivative. Czech J Phys 51, 1348–1354 (2001). https://doi.org/10.1023/A:1013378221617
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DOI: https://doi.org/10.1023/A:1013378221617