Browsing by Author "Golmankhaneh, Alireza Khalili"

Now showing 1 - 14 of 14

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; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 39
Citation - Scopus: 41
Diffusion on Middle- Cantor Sets
(Mdpi, 2018) Fernandez, Arran; Golmankhaneh, Ali Khalili; Baleanu, Dumitru; Golmankhaneh, Alireza Khalili; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 72
Citation - Scopus: 92
Fractional Electromagnetic Equations Using Fractional Forms
(Springer/plenum Publishers, 2009) Golmankhaneh, Ali Khalili; Golmankhaneh, Alireza Khalili; Baleanu, Mihaela Cristina; Baleanu, Dumitru; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 3
Citation - Scopus: 4
Fractional Odd-Dimensional Mechanics
(Springer international Publishing Ag, 2011) Golmankhaneh, Alireza Khalili; Baleanu, Dumitru; Baleanu, Mihaela Cristina; Golmankhaneh, Ali Khalili; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 14
Hamiltonian Structure of Fractional First Order Lagrangian
(Springer/plenum Publishers, 2010) Golmankhaneh, Alireza Khalili; Baleanu, Dumitru; Baleanu, Mihaela Cristina; Golmankhaneh, Ali Khalili; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 18
Citation - Scopus: 24
Lagrangian and Hamiltonian Mechanics on Fractals Subset of Real-Line
(Springer/plenum Publishers, 2013) Golmankhaneh, Ali Khalili; Baleanu, Dumitru; Golmankhaneh, Alireza Khalili; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.
Citation - WoS: 42
Citation - Scopus: 79
Local Fractional Sumudu Transform With Application To Ivps on Cantor Sets
(Hindawi Ltd, 2014) Golmankhaneh, Alireza Khalili; Baleanu, Dumitru; Yang, Xiao-Jun; Srivastava, H. M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Local fractional derivatives were investigated intensively during the last few years. The coupling method of Sumudu transform and local fractional calculus (called as the local fractional Sumudu transform) was suggested in this paper. The presented method is applied to find the non differentiable analytical solutions for initial value problems with local fractional derivative. The obtained results are given to show the advantages.
Citation - WoS: 31
Citation - Scopus: 36
New Derivatives on the Fractal Subset of Real-Line
(Mdpi, 2016) Baleanu, Dumitru; Golmankhaneh, Alireza Khalili; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace transformation is given and applied for solving linear and non-linear fractal equations. The advantage of using these new nonlocal derivatives on the fractals subset of real-line lies in the fact that they are better at modeling processes with memory effect.
Citation - WoS: 37
Citation - Scopus: 42
On Artificial Neural Networks Approach With New Cost Functions
(Elsevier Science inc, 2018) Jafarian, Ahmad; Nia, Safa Measoomy; Golmankhaneh, Alireza Khalili; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this manuscript, the artificial neural networks approach involving generalized sigmoid function as a cost function, and three-layered feed-forward architecture is considered as an iterative scheme for solving linear fractional order ordinary differential equations. The supervised back-propagation type learning algorithm based on the gradient descent method, is able to approximate this a problem on a given arbitrary interval to any desired degree of accuracy. To be more precise, some test problems are also given with the comparison to the simulation and numerical results given by another usual method. (C) 2018 Elsevier Inc. All rights reserved.
Citation - WoS: 13
Citation - Scopus: 10
On Fuzzy Fractional Laplace Transformation
(Hindawi Ltd, 2014) Golmankhaneh, Alireza Khalili; Baleanu, Dumitru; Jafarian, Ahmad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Fuzzy and fractional differential equations are used to model problems with uncertainty and memory. Using the fractional fuzzy Laplace transformation we have solved the fuzzy fractional eigenvalue differential equation. By illustrative examples we have shown the results.
Citation - WoS: 25
Citation - Scopus: 27
On the Fractional Hamilton and Lagrange Mechanics
(Springer/plenum Publishers, 2012) Yengejeh, Ali Moslemi; Baleanu, Dumitru; Golmankhaneh, Alireza Khalili; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The 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.
Citation - WoS: 21
Citation - Scopus: 25
Solving Fully Fuzzy Polynomials Using Feed-Back Neural Networks
(Taylor & Francis Ltd, 2015) Jafari, Raheleh; Golmankhaneh, Alireza Khalili; Baleanu, Dumitru; Jafarian, Ahmad; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Structure of Magnetic Field Lines
(Elsevier Science Bv, 2012) Golmankhaneh, Alireza Khalili; Jazayeri, Seyed Masud; Baleanu, Dumitru; Golmankhaneh, Ali Khalili; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.