Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Author: search.filters.author.Muslih, Sami I.Publication Index: search.filters.publicationIndex.WoS

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Now showing 1 - 10 of 28
  • Article
    Citation - WoS: 16
    Citation - Scopus: 23
    On 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.; Matematik
    The 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: 28
    Citation - Scopus: 33
    Lagrangian Formulation of Maxwell's Field in Fractional D Dimensional Space-Time
    (Editura Acad Romane, 2010) Muslih, Sami I.; Baleanu, Dumitru; Saddallah, Madhat; Baleanu, Dumitru; Rabei, Eqab; Matematik
    The Lagrangian formulation for field systems is obtained in fractional space-time fractional dimensions D = D-space + D-time. The equations of motion for Maxwell's field are obtained. It is shown that the form of Maxwell's equations in fractional dimensional space are not invariant and they can be solved in the same manner as in the integer space-time dimensions.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 2
    Solutions of Massless Conformal Scalar Field in an N-Dimensional Einstein Space
    (Jagiellonian Univ Press, 2008) Muslih, Sami I.; Baleanu, Dumitru; Baleanu, Dumitru; Rabei, Eqab M.; Matematik
    In this paper the wave equation for massless conformal scalar field in an Einstein's n-dimensional universe is solved and the eigen frequencies are obtained. The special case for alpha = 4 is recovered and the results are in exact agreement with those obtained in literature.
  • Article
    Citation - WoS: 18
    Citation - Scopus: 23
    Fractional Dimensional Harmonic Oscillator
    (Editura Acad Romane, 2011) Eid, R.; Baleanu, Dumitru; Muslih, Sami I.; Baleanu, Dumitru; Rabei, E.; Matematik
    The fractional Schrodinger equation corresponding to the fractional oscillator was investigated. The regular singular points and the exact solutions of the corresponding radial Schrodinger equation were reported.
  • Article
    Citation - WoS: 13
    Citation - Scopus: 15
    Mandelbrot Scaling and Parametrization Invariant Theories
    (Editura Acad Romane, 2010) Muslih, Sami I.; Baleanu, Dumitru; Baleanu, Dumitru; Matematik
    Fractional 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.
  • Conference Object
    Citation - WoS: 9
    Citation - Scopus: 11
    On Fractional Variational Principles
    (Springer, 2007) Muslih, Sami I.; Baleanu, Dumitru
    The 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: 11
    Citation - Scopus: 13
    Fractional 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: 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.