Browsing by Author "Rabei, Eqab M."

Now showing 1 - 20 of 21

Citation - WoS: 2
Citation - Scopus: 2
Comment On "Maxwell's Equations And Electromagnetic Lagrangian Density in Fractional Form" [J. Math. Phys. 53, 033505 ( 2012)]
(Amer inst Physics, 2014) Rabei, Eqab M.; Baleanu, Dumitru; Al-Jamel, A.; Widyan, H.; Baleanu, D.; 56389; Matematik
In a recent paper, Jaradat et al. [J. Math. Phys. 53, 033505 (2012)] have presented the fractional form of the electromagnetic Lagrangian density within the Riemann-Liouville fractional derivative. They claimed that the Agrawal procedure [O. P. Agrawal, J. Math. Anal. Appl. 272, 368 (2002)] is used to obtain Maxwell's equations in the fractional form, and the Hamilton's equations of motion together with the conserved quantities obtained from fractional Noether's theorem are reported. In this comment, we draw the attention that there are some serious steps of the procedure used in their work are not applicable even though their final results are correct. Their work should have been done based on a formulation as reported by Baleanu and Muslih [Phys. Scr. 72, 119 (2005)]. (C) 2014 AIP Publishing LLC.
Citation - WoS: 6
Citation - Scopus: 9
Extension of perturbation theory to quantum systems with conformable derivative
(World Scientific Publ Co Pte Ltd, 2021) Al-Masaeed, Mohamed; Baleanu, Dumitru; Rabei, Eqab M.; Al-Jamel, Ahmed; Baleanu, Dumitru; 56389; Matematik
In this paper, the perturbation theory is extended to be applicable for systems containing conformable derivative of fractional order alpha. This is needed as an essential and powerful approximation method for describing systems with conformable differential equations that are difficult to solve analytically. The work here is derived and discussed for the conformable Hamiltonian systems that appears in the conformable quantum mechanics. The required alpha-corrections for the energy eigenvalues and eigenfunctions are derived. To demonstrate this extension, three illustrative examples are given, and the standard values obtained by the traditional theory are recovered when alpha = 1.
Citation - WoS: 11
Citation - Scopus: 13
Fractional Hamilton's equations of motion in fractional time
(de Gruyter Poland Sp Z O O, 2007) Muslih, Sami I.; Baleanu, Dumitru; Baleanu, Dumitru; Rabei, Eqab M.; 56389; Matematik
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.
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.; 56389; Matematik
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: 0
Citation - Scopus: 0
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.; Matematik
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: 17
Citation - Scopus: 24
Fractional WKB approximation
(Springer, 2009) Rabei, Eqab M.; Baleanu, Dumitru; Altarazi, Ibrahim M. A.; Muslih, Sami I.; Baleanu, Dumitru; Matematik
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: 23
Citation - Scopus: 24
Gravitational potential in fractional space
(de Gruyter Open Ltd, 2007) Muslih, Sami I.; Baleanu, Dumitru; Baleanu, Dumitru; Rabei, Eqab M.; Matematik
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: 5
Citation - Scopus: 10
Hamilton formulation for continuous systems with second order derivatives
(Springer/plenum Publishers, 2008) El-Zalan, Hosam A.; Baleanu, Dumitru; Muslih, Sami I.; Rabei, Eqab M.; Baleanu, Dumitru; Matematik
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: 22
Citation - Scopus: 31
Hamilton-Jacobi and fractional like action with time scaling
(Springer, 2011) Herzallah, Mohamed A. E.; Baleanu, Dumitru; Muslih, Sami I.; Baleanu, Dumitru; Rabei, Eqab M.; Matematik
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.
Citation - WoS: 12
Citation - Scopus: 18
Hamilton-Jacobi formulation for systems in terms of Riesz's fractional derivatives
(Springer/plenum Publishers, 2011) Rabei, Eqab M.; Baleanu, Dumitru; Rawashdeh, Ibrahim M.; Muslih, Sami; Baleanu, Dumitru; Matematik
The paper presents fractional Hamilton-Jacobi formulations for systems containing Riesz fractional derivatives (RFD's). The Hamilton-Jacobi equations of motion are obtained. An illustrative example for simple harmonic oscillator (SHO) has been discussed. It was observed that the classical results are recovered for integer order derivatives.
Citation - WoS: 26
Citation - Scopus: 27
Hamilton-Jacobi formulation of systems within Caputo's fractional derivative
(Iop Publishing Ltd, 2008) Rabei, Eqab M.; Baleanu, Dumitru; Almayteh, Ibtesam; Muslih, Sami I.; Baleanu, Dumitru; Matematik
A new fractional Hamilton-Jacobi formulation for discrete systems in terms of fractional Caputo derivatives was developed. The fractional action function is obtained and the solutions of the equations of motion are recovered. Two examples are studied in detail.
Citation - WoS: 20
Citation - Scopus: 20
Heisenberg's equations of motion with fractional derivatives
(Sage Publications Ltd, 2007) Rabei, Eqab M.; Baleanu, Dumitru; Tarawneh, Derar M.; Muslih, Sami I.; Baleanu, Dumitru; Matematik
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.
Citation - WoS: 2
Citation - Scopus: 3
On fractional dynamics on the extended phase space
(Asme, 2010) Baleanu, Dumitru; Baleanu, Dumitru; Muslih, Sami I.; Rabei, Eqab M.; Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Matematik
Fractional 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]
Citation - WoS: 88
Citation - Scopus: 97
On fractional Euler-Lagrange and Hamilton equations and the fractional generalization of total time derivative
(Springer, 2008) Baleanu, Dumitru; Baleanu, Dumitru; Muslih, Sami I.; Rabei, Eqab M.; 56389; Matematik
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.
Citation - WoS: 0
Citation - Scopus: 0
On Fractional Hamilton Formulation Within Caputo Derivatives
(Amer Soc Mechanical Engineers, 2008) Baleanu, Dumitru; Muslih, Sami I.; Rabei, Eqab M.; Matematik
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.
On fractional Hamilton formulation within Caputo derivatives
(Amer Soc Mechanical Engineers, 2008) Baleanu, Dumitru; Muslih, Sami I.; Rabei, Eqab M.; 56389; Matematik
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: 16
Citation - Scopus: 22
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: 6
Citation - Scopus: 9
Quantization of fractional harmonic oscillator using creation and annihilation operators
(de Gruyter Poland Sp Z O O, 2021) Al-Masaeed, Mohamed; Baleanu, Dumitru; Rabei, Eqab M.; Al-Jamel, Ahmed; Baleanu, Dumitru; 56389; Matematik
In this article, the Hamiltonian for the conform-able harmonic oscillator used in the previous study [Chung WS, Zare S, Hassanabadi H, Maghsoodi E. The effect of fractional calculus on the formation of quantum-mechan-ical operators. Math Method Appl Sci. 2020;43(11):6950-67.] is written in terms of fractional operators that we called alpha-creation and alpha-annihilation operators. It is found that these operators have the following influence on the energy states. For a given order alpha, the alpha-creation operator pro-motes the state while the alpha-annihilation operator demotes the state. The system is then quantized using these crea-tion and annihilation operators and the energy eigenvalues and eigenfunctions are obtained. The eigenfunctions are expressed in terms of the conformable Hermite func-tions. The results for the traditional quantum harmonic oscillator are found to be recovered by setting alpha = 1.
Citation - WoS: 8
Citation - Scopus: 12
Quantization of fractional systems using WKB approximation
(Elsevier, 2010) Rabei, Eqab M.; Baleanu, Dumitru; Muslih, Sami I.; Baleanu, Dumitru; Matematik
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.
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.; 56389; 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.