WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Conference Object Citation - WoS: 9Citation - Scopus: 11On Fractional Variational Principles(Springer, 2007) Muslih, Sami I.; Baleanu, DumitruThe paper provides the fractional Lagrangian and Hamiltonian formulations of mechanical and field systems. The fractional treatment of constrained system is investigated together with the fractional path integral analysis. Fractional Schrodinger and Dirac fields are analyzed in details.Article Citation - WoS: 88Citation - Scopus: 98On Fractional Euler-Lagrange and Hamilton Equations and the Fractional Generalization of Total Time Derivative(Springer, 2008) Muslih, Sami I.; Rabei, Eqab M.; Baleanu, DumitruFractional mechanics describe both conservative and nonconservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics, the equivalent Lagrangians play an important role because they admit the same Euler-Lagrange equations. By adding a total time derivative of a suitable function to a given classical Lagrangian or by multiplying with a constant, the Lagrangian we obtain are the same equations of motion. In this study, the fractional discrete Lagrangians which differs by a fractional derivative are analyzed within Riemann-Liouville fractional derivatives. As a consequence of applying this procedure, the classical results are reobtained as a special case. The fractional generalization of Faa di Bruno formula is used in order to obtain the concrete expression of the fractional Lagrangians which differs from a given fractional Lagrangian by adding a fractional derivative. The fractional Euler-Lagrange and Hamilton equations corresponding to the obtained fractional Lagrangians are investigated, and two examples are analyzed in detail.Article Citation - WoS: 22Citation - Scopus: 31Hamilton-Jacobi and Fractional Like Action With Time Scaling(Springer, 2011) Muslih, Sami I.; Baleanu, Dumitru; Rabei, Eqab M.; Herzallah, Mohamed A. E.This paper represents the Hamilton-Jacobi formulation for fractional variational problem with fractional like action written as an integration over a time scaling parameter. Also we developed the fractional Hamiltonian formulation for the fractional like action. In all the given calculations, the most popular Riemann-Liouville (RL) and Caputo fractional derivatives are employed. An example illustrates our approach.Article Citation - WoS: 18Citation - Scopus: 26Fractional Wkb Approximation(Springer, 2009) Altarazi, Ibrahim M. A.; Muslih, Sami I.; Baleanu, Dumitru; Rabei, Eqab M.Wentzel-Kramer-Brillouin (WKB) approximation for fractional systems is investigated in this paper using the fractional calculus. In the fractional case, the wave function is constructed such that the phase factor is the same as the Hamilton's principle function S. To demonstrate our proposed approach, two examples are investigated in detail.