WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 19Citation - Scopus: 25Lagrangian and Hamiltonian Mechanics on Fractals Subset of Real-Line(Springer/plenum Publishers, 2013) Golmankhaneh, Ali Khalili; Baleanu, Dumitru; Golmankhaneh, Alireza KhaliliA discontinuous media can be described by fractal dimensions. Fractal objects has special geometric properties, which are discrete and discontinuous structure. A fractal-time diffusion equation is a model for subdiffusive. In this work, we have generalized the Hamiltonian and Lagrangian dynamics on fractal using the fractional local derivative, so one can use as a new mathematical model for the motion in the fractal media. More, Poisson bracket on fractal subset of real line is suggested.Article Citation - WoS: 34Citation - Scopus: 38Fractional Pais-Uhlenbeck Oscillator(Springer/plenum Publishers, 2012) Petras, Ivo; Asad, Jihad H.; Pilar Velasco, Maria; Baleanu, Dumitru; Velasco, Maria PilarIn this paper we study the fractional Lagrangian of Pais-Uhlenbeck oscillator. We obtained the fractional Euler-Lagrangian equation of the system and then we studied the obtained Euler-Lagrangian equation numerically. The numerical study is based on the so-called Grunwald-Letnikov approach, which is power series expansion of the generating function (backward and forward difference) and it can be easy derived from the Grunwald-Letnikov definition of the fractional derivative. This approach is based on the fact, that Riemman-Liouville fractional derivative is equivalent to the Grunwald-Letnikov derivative for a wide class of the functions.Article Citation - WoS: 27Citation - Scopus: 31The Dual Action of Fractional Multi Time Hamilton Equations(Springer/plenum Publishers, 2009) Golmankhaneh, Ali Khalili; Golmankhaneh, Alireza Khalili; Baleanu, DumitruThe fractional multi time Lagrangian equations has been derived for dynamical systems within Riemann-Liouville derivatives. The fractional multi time Hamiltonian is introduced as Legendre transformation of multi time Lagrangian. The corresponding fractional Euler-Lagrange and the Hamilton equations are obtained and the fractional multi time constant of motion are discussed.Article Citation - WoS: 20Citation - Scopus: 28About Schrodinger Equation on Fractals Curves Imbedding in R <sup>3</Sup>(Springer/plenum Publishers, 2015) Golmankhaneh, Ali Khalili; Baleanu, Dumitru; Golmankhaneh, Alireza KhaliliIn this paper we introduced the quantum mechanics on fractal time-space. In a suggested formalism the time and space vary on Cantor-set and Von-Koch curve, respectively. Using Feynman path method in quantum mechanics and F (alpha) -calculus we find SchrA << dinger equation on on fractal time-space. The Hamiltonian and momentum fractal operator has been indicated. More, the continuity equation and the probability density is given in view of F (alpha) -calculus.Article Citation - WoS: 25Citation - Scopus: 27On the Fractional Hamilton and Lagrange Mechanics(Springer/plenum Publishers, 2012) Yengejeh, Ali Moslemi; Baleanu, Dumitru; Golmankhaneh, Alireza KhaliliThe fractional generalization of Hamiltonian mechanics is constructed by using the Lagrangian involving fractional derivatives. In this paper the equation of projectile motion with air friction using fractional Hamiltonian mechanics and equation for current loop involving electric source, a resistor, an inductor and a capacitor has been obtained. Furthermore, fractional optics has been introduced.Article Citation - WoS: 18Citation - Scopus: 22Fedosov Quantization of Fractional Lagrange Spaces(Springer/plenum Publishers, 2011) Vacaru, Sergiu I.; Baleanu, DumitruThe main goal of this work is to perform a nonholonomic deformation (Fedosov type) quantization of fractional Lagrange-Finsler geometries. The constructions are provided for a fractional almost Kahler model encoding equivalently all data for fractional Euler-Lagrange equations with Caputo fractional derivative.Article Citation - WoS: 14Citation - Scopus: 20Hamilton-Jacobi Formulation for Systems in Terms of Riesz's Fractional Derivatives(Springer/plenum Publishers, 2011) Rawashdeh, Ibrahim M.; Muslih, Sami; Baleanu, Dumitru; Rabei, Eqab M.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.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: 14Hamiltonian Structure of Fractional First Order Lagrangian(Springer/plenum Publishers, 2010) Golmankhaneh, Alireza Khalili; Baleanu, Dumitru; Baleanu, Mihaela Cristina; Golmankhaneh, Ali KhaliliIn this paper, we show that the fractional constraint Hamiltonian formulation, using Dirac brackets, leads to the same equations as those obtained from fractional Euler-Lagrange equations. Furthermore, the fractional Faddeev-Jackiw formalism was constructed.Article Citation - WoS: 33Citation - Scopus: 35Is It Possible To Derive Newtonian Equations of Motion With Memory(Springer/plenum Publishers, 2010) Baleanu, D.; Nigmatullin, R. R.In this paper for a given example we proved that the Riemann-Liouville fractional integral term appears naturally and relates the external force with acceleration within the fractional Newtonian equation. The consideration of some self-similar process that leads to the fractional integral as well as some possible generalizations of the proposed model was discussed.