Browsing by Author "Muslih, Sami I."

Now showing 1 - 20 of 32

Citation - WoS: 8
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.
Citation - WoS: 32
Citation - Scopus: 35
Fractional 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.
On Fractional Hamilton Formulation Within Caputo Derivatives
(Amer Soc Mechanical Engineers, 2008) Baleanu, Dumitru; Muslih, Sami I.; Rabei, Eqab M.
The fractional Lagrangian and Hamiltonian dynamics is an important issue in fractional calculus area. The classical dynamics can be reformulated in terms of fractional derivatives. The fractional variational principles produce fractional Euler-Lagrange equations and fractional Hamiltonian equations. The fractional dynamics strongly depends of the fractional integration by parts as well as the non-locality of the fractional derivatives. In this paper we present the fractional Hamilton formulation based on Caputo fractional derivatives. One example is treated in details to show the characteristics of the fractional dynamics.
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.
Citation - WoS: 27
Citation - Scopus: 32
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.
Citation - WoS: 165
Citation - Scopus: 189
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.
Citation - WoS: 53
Citation - Scopus: 65
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.
Citation - WoS: 5
Citation - Scopus: 10
Hamilton 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.
Citation - WoS: 55
Citation - Scopus: 67
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.
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.
Citation - WoS: 68
Citation - Scopus: 69
Fractional Hamiltonian Analysis of Higher Order Derivatives Systems
(Aip Publishing, 2006) Tas, Kenan; Baleanu, Dumitru; Muslih, Sami I.
The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives. (c) 2006 American Institute of Physics.
Citation - WoS: 23
Citation - Scopus: 24
Gravitational Potential in Fractional Space
(de Gruyter Open Ltd, 2007) Baleanu, Dumitru; Rabei, Eqab M.; Muslih, Sami I.
In this paper the gravitational potential with beta-th order fractional mass distribution was obtained in a dimensionally fractional space. We show that the fractional gravitational universal constant G(alpha) is given by G(alpha) = 2 Gamma(alpha/2)/Pi(alpha/2-1)(alpha-2) G, where G is the usual gravitational universal constant and the dimensionality of the space is alpha > 2. (c) Versita Warsaw and Springer-Verlag Berlin Heidelberg. All rights reserved.
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.
Citation - WoS: 17
Citation - Scopus: 22
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.
Citation - WoS: 63
Citation - Scopus: 77
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.
Citation - WoS: 26
A 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.
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.
Fractional mechanics on the extended phase space
(Amer Soc Mechanical Engineers, 2010) Baleanu, Dumitru; Muslih, Sami I.; Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Rabei, Eqab M.
Fractional calculus has gained a lot of importance and potential applications in several areas of science and engineering. The fractional dynamics and the fractional variational principles started to be used intensively as an alternative tool in order to describe the physical complex phenomena. In this paper we have discussed the fractional extension of the classical dynamics. The fractional Hamiltonian is constructed and the fractional generalized Poisson's brackets on the extended phase space is established.
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.
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.