WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

Browse

Filters

2007 - 200962010 - 20114

Settings

Author: search.filters.author.Muslih, Sami I.WoS Q: search.filters.wosQuartile.Q1

Search Results

Now showing 1 - 10 of 10
  • Article
    Citation - WoS: 88
    Citation - Scopus: 98
    On Fractional Euler-Lagrange and Hamilton Equations and the Fractional Generalization of Total Time Derivative
    (Springer, 2008) Muslih, Sami I.; Rabei, Eqab M.; Baleanu, Dumitru
    Fractional 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: 22
    Citation - Scopus: 31
    Hamilton-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: 9
    Citation - Scopus: 8
    Fractional Time Action and Perturbed Gravity
    (World Scientific Publ Co Pte Ltd, 2011) Muslih, Sami I.; Baleanu, Dumitru; Rabei, Eqab; Sadallah, Madhat
    In 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: 63
    Citation - Scopus: 76
    Generalized 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: 8
    Citation - Scopus: 12
    Quantization of Fractional Systems Using Wkb Approximation
    (Elsevier, 2010) Muslih, Sami I.; Baleanu, Dumitru; Rabei, Eqab M.
    The Caputo's fractional derivative is used to quantize fractional systems using (WKB) approximation. The wave function is build such that the phase factor is the same as the Hamilton's principle function S. The energy eigenvalue is found to be in exact agreement with the classical case. To demonstrate our approach an example is investigated in details. (C) 2009 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 18
    Citation - Scopus: 26
    Fractional 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.
  • Article
    Citation - WoS: 54
    Citation - Scopus: 66
    On Fractional Schrodinger Equation in Α-Dimensional Fractional Space
    (Pergamon-elsevier Science Ltd, 2009) Muslih, Sami I.; Baleanu, Dumitru; Rabei, E.; Eid, Rajeh
    The 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.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 5
    Fractional Euler-Lagrange and Fractional Hamilton Equations for Super Symmetric Classical Model
    (World Scientific Publ Co Pte Ltd, 2007) Muslih, Sami I.; Baleanu, Dumitru
    Fractional 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.
  • Article
    Citation - WoS: 168
    Citation - Scopus: 192
    The Hamilton Formalism With Fractional Derivatives
    (Academic Press inc Elsevier Science, 2007) Nawafleh, Khaled I.; Hijjawi, Raed S.; Muslih, Sami I.; Baleanu, Dumitru; Rabei, Eqab M.
    Recently the traditional calculus of variations has been extended to be applicable for systems containing fractional derivatives. In this paper the passage from the Lagrangian containing fractional derivatives to the Hamiltonian is achieved. The Hamilton's equations of motion are obtained in a similar manner to the usual mechanics. In addition, the classical fields with fractional derivatives are investigated using Hamiltonian formalism. Two discrete problems and one continuous are considered to demonstrate the application of the formalism, the results are obtained to be in exact agreement with Agrawal's formalism. (c) 2006 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 56
    Citation - Scopus: 68
    Fractional Multipoles in Fractional Space
    (Pergamon-elsevier Science Ltd, 2007) Baleanu, Dumitru; Muslih, Sami I.
    Gauss' law in alpha-dimensional fractional space is investigated. The electrostatic potential with beta th-order fractional multipole is obtained in alpha-dimensionally fractional space. (c) 2005 Elsevier Ltd. All rights reserved.