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: 23Citation - Scopus: 23Conditional Optimization Problems: Fractional Order Case(Springer/plenum Publishers, 2013) Baleanu, Dumitru; Majd, Vahid Johari; Razminia, AbolhassanIn this manuscript, we introduce a new formulation for the constrained optimization problems in which the objective function is considered in the fractional integral form. The constraints are applied in two separate cases, namely, fractional differential and fractional isoperimetric constraints. In both cases, by using the extended Euler-Lagrange equations and the Lagrange multiplier method, the necessary conditions are obtained. An example is given in order to illustrate the effectiveness of the reported results.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: 44Citation - Scopus: 52New Numerical Approach for Fractional Variational Problems Using Shifted Legendre Orthonormal Polynomials(Springer/plenum Publishers, 2017) Hafez, Ramy M.; Bhrawy, Ali H.; Baleanu, Dumitru; El-Kalaawy, Ahmed A.; Ezz-Eldien, Samer S.This paper reports a new numerical approach for numerically solving types of fractional variational problems. In our approach, we use the fractional integrals operational matrix, described in the sense of Riemann-Liouville, with the help of the Lagrange multiplier technique for converting the fractional variational problem into an easier problem that consisting of solving an algebraic equations system in the unknown coefficients. Several numerical examples are introduced, combined with their approximate solutions and comparisons with other numerical approaches, for confirming the accuracy and applicability of the proposed approach.Article Citation - WoS: 80Citation - Scopus: 93A New Formulation of the Fractional Optimal Control Problems Involving Mittag-Leffler Nonsingular Kernel(Springer/plenum Publishers, 2017) Jajarmi, Amin; Hajipour, Mojtaba; Baleanu, DumitruThe aim of this paper is to propose a new formulation of the fractional optimal control problems involving Mittag-Leffler nonsingular kernel. By using the Lagrange multiplier within the calculus of variations and by applying the fractional integration by parts, the necessary optimality conditions are derived in terms of a nonlinear two-point fractional boundary value problem. Based on the convolution formula and generalized discrete Gronwall's inequality, the numerical scheme for solving this problem is developed and its convergence is proved. Numerical simulations and comparative results show that the suggested technique is efficient and provides satisfactory results.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.