The types of derivatives and bifurcation in fractional mechanics

In this paper we are to define a new velocity having a dimension of (Length)α=(Time) and a new acceleration having a dimension of (Length)α=(Time)2, based on the fractional addition rule. Using this we discuss the fractional mechanics in one dimension. We show the conservation of fractional energy and formulate the Hamiltonian formalism for fractional mechanics. We exhibit some examples of fractional mechanics.

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Solutions of Euler-Lagrange equations in fractional mechanics

10.1063/1.2820982 ◽

2007 ◽

Cited By ~ 7

Author(s):

M. Klimek ◽

Piotr Kielanowski ◽

Anatol Odzijewicz ◽

Martin Schlichenmeier ◽

Theodore Voronov

Keyword(s):

Lagrange Equations ◽

Fractional Mechanics

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Fractional Mechanics on the Extended Phase Space

Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C ◽

10.1115/detc2009-86586 ◽

2009 ◽

Cited By ~ 1

Author(s):

Dumitru Baleanu ◽

Sami I. Muslih ◽

Alireza K. Golmankhaneh ◽

Ali K. Golmankhaneh ◽

Eqab M. Rabei

Keyword(s):

Phase Space ◽

Variational Principles ◽

Fractional Dynamics ◽

Classical Dynamics ◽

Extended Phase Space ◽

Science And Engineering ◽

Extended Phase ◽

Potential Applications ◽

Fractional Mechanics ◽

Complex Phenomena

Fractional calculus has gained a lot of importance and potential applications in several areas of science and engineering. The fractional dynamics and the fractional variational principles started to be used intensively as an alternative tool in order to describe the physical complex phenomena. In this paper we have discussed the fractional extension of the classical dynamics. The fractional Hamiltonian is constructed and the fractional generalized Poisson’s brackets on the extended phase space is established.

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