Abstract
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.
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Klimek, M. Lagrangean and Hamiltonian fractional sequential mechanics. Czech J Phys 52, 1247–1253 (2002). https://doi.org/10.1023/A:1021389004982
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DOI: https://doi.org/10.1023/A:1021389004982