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On Fractional Hamilton Formulation Within Caputo Derivatives
(Amer Soc Mechanical Engineers, 2008) Baleanu, Dumitru; Muslih, Sami I.; Rabei, Eqab M.
The fractional Lagrangian and Hamiltonian dynamics is an important issue in fractional calculus area. The classical dynamics can be reformulated in terms of fractional derivatives. The fractional variational principles produce fractional Euler-Lagrange equations and fractional Hamiltonian equations. The fractional dynamics strongly depends of the fractional integration by parts as well as the non-locality of the fractional derivatives. In this paper we present the fractional Hamilton formulation based on Caputo fractional derivatives. One example is treated in details to show the characteristics of the fractional dynamics.
Citation - WoS: 5
Citation - Scopus: 6
Lagrangians With Linear Velocities Within Hilfer Fractional Derivative
(Amer Soc Mechanical Engineers, 2012) Baleanu, Dumitru; Agrawal, Om P.; Muslih, Sami I.
Fractional variational principles started to be one of the major area in the field of fractional calculus. During the last few years the fractional variational principles were developed within several fractional derivatives. One of them is the Hilfer's generalized fractional derivative which interpolates between Riemann-Liouville and Caputo fractional derivatives. In this paper the fractional Euler-Lagrange equations of the Lagrangians with linear velocities are obtained within the Hilfer fractional derivative.

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