WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 16Citation - Scopus: 23On Fractional Hamiltonian Systems Possessing First-Class Constraints Within Caputo Derivatives(Editura Acad Romane, 2011) Baleanu, Dumitru; Baleanu, Dumitru; Muslih, Sami I.; Rabei, Eqab M.; Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; MatematikThe fractional constrained systems possessing only first class constraints are analyzed within Caputo fractional derivatives. It was proved that the fractional Hamilton-Jacobi like equations appear naturally in the process of finding the full canonical transformations. An illustrative example is analyzed.Article Citation - WoS: 13Citation - Scopus: 15Mandelbrot Scaling and Parametrization Invariant Theories(Editura Acad Romane, 2010) Muslih, Sami I.; Baleanu, Dumitru; Baleanu, Dumitru; MatematikFractional variational principles have gained considerable importance during the last decade due to their applications in several areas of sciences and engineering. In this paper we will adapt this variational principle to obtain the Euler-Lagrange equation of motion, by considering two different cases. In the first case we used the scaling concepts of Mandelbrot of fractals in variational problems of mechanical systems in order to re-write the action function as an integration over a scaling measure. After that we parameterize the time in the action integral to obtain the equations of motion. It is shown that the genuine Euler-Lagrange equations of motion are those which are obtained using the Mandelbrot scaling of space/and or time.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: 2Citation - Scopus: 3On Fractional Dynamics on the Extended Phase Space(Asme, 2010) Muslih, Sami I.; Rabei, Eqab M.; Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Baleanu, DumitruFractional calculus should be applied to various dynamical systems in order to be validated in practice. On this line of taught, the fractional extension of the classical dynamics is introduced. The fractional Hamiltonian on the extended phase space is analyzed and the corresponding generalized Poisson's brackets are constructed. [DOI: 10.1115/1.4002091]Article Citation - WoS: 72Citation - Scopus: 83A Fractional Schrodinger Equation and Its Solution(Springer/plenum Publishers, 2010) Agrawal, Om P.; Baleanu, Dumitru; Muslih, Sami I.This paper presents a fractional Schrodinger equation and its solution. The fractional Schrodinger equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives to obtain the fractional Euler-Lagrange equations of motion. We present the Lagrangian for the fractional Schrodinger equation of order alpha. We also use a fractional Klein-Gordon equation to obtain the fractional Schrodinger equation which is the same as that obtained using the fractional variational principle. As an example, we consider the eigensolutions of a particle in an infinite potential well. The solutions are obtained in terms of the sines of the Mittag-Leffler function.Article Citation - WoS: 26A Fractional Dirac Equation and Its Solution(Iop Publishing Ltd, 2010) Agrawal, Om P.; Baleanu, Dumitru; Muslih, Sami I.This paper presents a fractional Dirac equation and its solution. The fractional Dirac equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives. By applying the variational principle to a fractional action S, we obtain the fractional Euler-Lagrange equations of motion. We present a Lagrangian and a Hamiltonian for the fractional Dirac equation of order a. We also use a fractional Klein-Gordon equation to obtain the fractional Dirac equation which is the same as that obtained using the fractional variational principle. Eigensolutions of this equation are presented which follow the same approach as that for the solution of the standard Dirac equation. We also provide expressions for the path integral quantization for the fractional Dirac field which, in the limit a. 1, approaches to the path integral for the regular Dirac field. It is hoped that the fractional Dirac equation and the path integral quantization of the fractional field will allow further development of fractional relativistic quantum mechanics.Article Citation - WoS: 54Citation - Scopus: 66On Fractional Schrodinger Equation in Α-Dimensional Fractional Space(Pergamon-elsevier Science Ltd, 2009) Muslih, Sami I.; Baleanu, Dumitru; Rabei, E.; Eid, RajehThe Schrodinger equation is solved in a-dimensional fractional space with a Coulomb potential proportional to 1/r(beta-2), 2 <= beta <= 4. The wave functions are studied in terms of spatial dimensionality alpha and beta and the results for beta = 3 are compared with those obtained in the literature. (C) 2008 Elsevier Ltd. All rights reserved.Conference Object Citation - WoS: 7Citation - Scopus: 7Nonconservative Systems Within Fractional Generalized Derivatives(Sage Publications Ltd, 2008) Baleanu, Dumitru; Muslih, Sami I.A fractional derivative generalizes an ordinary derivative, and therefore the derivative of the product of two functions differs from that for the classical ( integer) case ; the integration by parts for Riemann-Liouville fractional derivatives involves both the left and right fractional derivatives. Despite these restrictions, fractional calculus models are good candidates for description of nonconservative systems. In this article, nonconservative Lagrangian mechanics are investigated within the fractional generalized derivative approach. The fractional Euler-Lagrange equations based on the Riemann-Liouville fractional derivatives are briefly presented. Using generalized fractional derivatives, we give a meaning for the term which appears in fractional Euler-Lagrange equations and contains the second order fractional derivative. The fractional Lagrangians and Hamiltonians of two illustrative nonconservative mechanical systems are investigated in detail.Article Citation - WoS: 6Citation - Scopus: 11Hamilton Formulation for Continuous Systems With Second Order Derivatives(Springer/plenum Publishers, 2008) Muslih, Sami I.; Rabei, Eqab M.; Baleanu, Dumitru; El-Zalan, Hosam A.In this paper the Hamilton formulation for continuous systems with second order derivatives has been developed. We generalized the Hamilton formulation for continuous systems with second order derivatives and apply this new formulation to Podolsky generalized electrodynamics, comparing with the results obtained through Dirac's method.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.