Browsing by Author "Golmankhaneh, Ali Khalili"

Now showing 1 - 11 of 11

Citation - WoS: 20
Citation - Scopus: 28
About Schrodinger Equation on Fractals Curves Imbedding in R ³
(Springer/plenum Publishers, 2015) Golmankhaneh, Ali Khalili; Baleanu, Dumitru; Golmankhaneh, Alireza Khalili
In 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.
Citation - WoS: 2
Citation - Scopus: 3
Brownian Motion on Cantor Sets
(Walter de Gruyter Gmbh, 2020) Ashrafi, Saleh; Baleanu, Dumitru; Fernandez, Arran; Golmankhaneh, Ali Khalili; Khalili Golmankhaneh, Ali
In this paper, we have investigated the Langevin and Brownian equations on fractal time sets using F-alpha-calculus and shown that the mean square displacement is not varied linearly with time. We have also generalized the classical method of deriving the Fokker Planck equation in order to obtain the Fokker-Planck equation on fractal time sets.
Citation - WoS: 45
Citation - Scopus: 47
Diffusion on Middle- Cantor Sets
(Mdpi, 2018) Fernandez, Arran; Golmankhaneh, Ali Khalili; Baleanu, Dumitru; Golmankhaneh, Alireza Khalili
In this paper, we study C-calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions. Functions with fractal support are not differentiable or integrable in terms of standard calculus, so we must involve local fractional derivatives. We have generalized the C-calculus on the generalized Cantor sets known as middle- Cantor sets. We have suggested a calculus on the middle- Cantor sets for different values of with 0<<1. Differential equations on the middle- Cantor sets have been solved, and we have presented the results using illustrative examples. The conditions for super-, normal, and sub-diffusion on fractal sets are given.
Citation - WoS: 27
Citation - Scopus: 31
The Dual Action of Fractional Multi Time Hamilton Equations
(Springer/plenum Publishers, 2009) Golmankhaneh, Ali Khalili; Golmankhaneh, Alireza Khalili; Baleanu, Dumitru
The 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.
Citation - WoS: 73
Citation - Scopus: 94
Fractional Electromagnetic Equations Using Fractional Forms
(Springer/plenum Publishers, 2009) Golmankhaneh, Ali Khalili; Golmankhaneh, Alireza Khalili; Baleanu, Mihaela Cristina; Baleanu, Dumitru
The generalized physics laws involving fractional derivatives give new models and conceptions that can be used in complex systems having memory effects. Using the fractional differential forms, the classical electromagnetic equations involving the fractional derivatives have been worked out. The fractional conservation law for the electric charge and the wave equations were derived by using this method. In addition, the fractional vector and scalar potentials and the fractional Poynting theorem have been derived.
Citation - WoS: 4
Citation - Scopus: 4
Fractional Odd-Dimensional Mechanics
(Springer international Publishing Ag, 2011) Golmankhaneh, Alireza Khalili; Baleanu, Dumitru; Baleanu, Mihaela Cristina; Golmankhaneh, Ali Khalili; Khalili Golmankhaneh, Ali
The classical Nambu mechanics is generalized to involve fractional derivatives using two different methods. The first method is based on the definition of fractional exterior derivative and the second one is based on extending the standard velocities to the fractional ones. Fractional Nambu mechanics may be used for nonintegrable systems with memory. Further, Lagrangian which is generate fractional Nambu equations is defined.
Citation - WoS: 2
Citation - Scopus: 2
Generalized Master Equation, Bohr's Model, and Multipoles on Fractals
(Editura Acad Romane, 2017) Ashrafi, Saleh; Baleanu, Dumitru; Golmankhaneh, Ali Khalili; Baleanu, Dumitru; Matematik
In this manuscript, we extend the F-alpha-calculus by suggesting theorems analogous to the Green's and the Stokes' ones. Utilizing the F-alpha-calculus, the classical multipole moments are generalized to fractal distributions. In addition, the generalized model for the Bohr's energy loss involving heavy charged particles is given.
Generalized master equation, bohr’s model, and multipoles on fractals
(2017) Ashrafi, Saleh; Golmankhaneh, Ali Khalili; Baleanu, Dumitru
In this manuscript, we extend the Fα-calculus by suggesting theorems analogous to the Green’s and the Stokes’ ones. Utilizing the Fα-calculus, the classical multipole moments are generalized to fractal distributions. In addition, the generalized model for the Bohr’s energy loss involving heavy charged particles is given. © 2017, Editura Academiei Romane. All Rights Reserved.
Citation - WoS: 14
Hamiltonian Structure of Fractional First Order Lagrangian
(Springer/plenum Publishers, 2010) Golmankhaneh, Alireza Khalili; Baleanu, Dumitru; Baleanu, Mihaela Cristina; Golmankhaneh, Ali Khalili
In 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.
Citation - WoS: 19
Citation - Scopus: 25
Lagrangian and Hamiltonian Mechanics on Fractals Subset of Real-Line
(Springer/plenum Publishers, 2013) Golmankhaneh, Ali Khalili; Baleanu, Dumitru; Golmankhaneh, Alireza Khalili
A 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.
Structure of Magnetic Field Lines
(Elsevier Science Bv, 2012) Golmankhaneh, Alireza Khalili; Jazayeri, Seyed Masud; Baleanu, Dumitru; Golmankhaneh, Ali Khalili
In this paper the Hamiltonian structure of magnetic lines is studied in many ways. First it is used vector analysis for defining the Poisson bracket and Casimir variable for this system. Second it is derived Pfaffian equations for magnetic field lines. Third, Lie derivative and derivative of Poisson bracket is used to show structure of this system. Finally, it is shown Nambu structure of the magnetic field lines. (C) 2011 Elsevier B.V. All rights reserved.