Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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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: 11Citation - Scopus: 13Fractional Hamilton's Equations of Motion in Fractional Time(de Gruyter Poland Sp Z O O, 2007) Baleanu, Dumitru; Rabei, Eqab M.; Muslih, Sami I.The Hamiltonian formulation for mechanical systems containing Riemman-Liouville fractional derivatives are investigated in fractional time. The fractional Hamilton's equations are obtained and two examples are investigated in detail. (C) Versita Warsaw and Springer-Verlag Berlin Heidelberg. All rights reserved.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: 9Citation - Scopus: 8Fractional Time Action and Perturbed Gravity(World Scientific Publ Co Pte Ltd, 2011) Muslih, Sami I.; Baleanu, Dumitru; Rabei, Eqab; Sadallah, MadhatIn this paper, we used the scaling concepts of Mandelbrot of fractals in variational problems of mechanical systems in order to re-write the action integral function as an integration over the fractional time. In addition, by applying the variational principle to this new fractional action, we obtained the modified Euler-Lagrange equations of motion in any fractional time of order 0 < alpha <= 1. Two examples are investigated in detail.Article Citation - WoS: 63Citation - Scopus: 76Generalized Variational Calculus in Terms of Multi-Parameters Fractional Derivatives(Elsevier Science Bv, 2011) Muslih, Sami I.; Baleanu, Dumitru; Agrawal, Om P.In this paper, we briefly introduce two generalizations of work presented a few years ago on fractional variational formulations. In the first generalization, we consider the Hilfer's generalized fractional derivative that in some sense interpolates between Riemann-Liouville and Caputo fractional derivatives. In the second generalization, we develop a fractional variational formulation in terms of a three parameter fractional derivative. We develop integration by parts formulas for the generalized fractional derivatives which are key to developing fractional variational calculus. It is shown that many derivatives used recently and their variational formulations can be obtained by setting different parameters to different values. We also define fractional generalized momenta and provide fractional Hamiltonian formulations in terms of the new generalized derivatives. An example is presented to show applications of the formulations presented here. Some possible extensions of this research are also discussed. (C) 2011 Elsevier B.V. All rights reserved.Article Citation - WoS: 2Citation - Scopus: 5Fractional Euler-Lagrange and Fractional Hamilton Equations for Super Symmetric Classical Model(World Scientific Publ Co Pte Ltd, 2007) Muslih, Sami I.; Baleanu, DumitruFractional Euler-Lagrange equations were investigated in the presence of the elements of Berezin algebra. The super fractional Hessian was defined and the fractional Hamiltonian of the super symmetric classical model was constructed.Conference Object Citation - WoS: 33Citation - Scopus: 35Fractional Euler-Lagrange Equations of Motion in Fractional Space(Sage Publications Ltd, 2007) Baleanu, Dumitru; Muslih, Sami I.Fractional variational principles have gained considerable importance during the last decade due to their various applications in several areas of science and engineering. In this study, the fractional Euler-Lagrange equations corresponding to a prescribed fractional space are obtained. These equations are obtained using the traditional method of calculus of variations adapted to the case of fractional space. The most general fractional Lagrangian is considered and the limit case when the parameters involved in fractional derivatives are equal to one, is obtained. Two examples are investigated in this study, namely the free particle on fractional space and the fractional simple pendulum, and their corresponding fractional Euler-Lagrange equations ar obtained.Conference Object Citation - WoS: 20Citation - Scopus: 20Heisenberg's Equations of Motion With Fractional Derivatives(Sage Publications Ltd, 2007) Tarawneh, Derar M.; Muslih, Sami I.; Baleanu, Dumitru; Rabei, Eqab M.Fractional variational principles is a new topic in the field of fractional calculus and it has been subject to intense debate during the last few years. One of the important applications of fractional variational principles is fractional quantization. In this present study, fractional calculus is applied to obtain the Hamiltonian formalism of non-conservative systems. The definition of Poisson bracket is used to obtain the equations of motion in terms of these brackets. The commutation relations and the Heisenberg equations of motion are also obtained. The proposed approach was tested on two examples and good agreements with the classical fractional are reported.