WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 11Citation - Scopus: 15Heat and Maxwell's Equations on Cantor Cubes(Editura Acad Romane, 2017) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Baleanu, Dumitru; MatematikThe fractal physics is an important research domain due to its scaling properties that can be seen everywhere in the nature. In this work, the generalized Maxwell's equations are given using fractal differential equations on the Cantor cubes and the electric field for the fractal charge distribution is derived. Moreover, the fractal heat equation is defined, which can be an adequate mathematical model for describing the flowing of the heat energy in fractal media. The suggested models are solved and the plots of the corresponding solutions are presented. A few illustrative examples are given to demonstrate the application of the obtained results in solving diverse physical problems.Article Citation - WoS: 14Citation - Scopus: 25On a New Measure on Fractals(Springer, 2013) Baleanu, Dumitru; Golmankhaneh, Alireza K.Fractals are sets whose Hausdorff dimension strictly exceeds their topological dimension. The algorithmic Riemannian-like method, F-alpha-calculus, has been suggested very recently. Henstock-Kurzweil integral is the generalized Riemann integral method by using the gauge function. In this paper we generalize the F-alpha-calculus as a fractional local calculus that is more suitable to describe some physical process. We introduce the new measure using the gauge function on fractal sets that gives a finer dimension in comparison with the Hausdorff and box dimension. Hilbert F-alpha-spaces are defined. We suggest the self-adjoint F-alpha-differential operator so that it can be applied in the fractal quantum mechanics and on the fractal curves.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: 23Citation - Scopus: 29Diffraction From Fractal Grating Cantor Sets(Taylor & Francis Ltd, 2016) Baleanu, D.; Golmankhaneh, Alireza K.In this paper, we have generalized the Fa-calculus by suggesting Fourier and Laplace transformations of the function with support of the fractals set which are the subset of the real line. Using this generalization, we have found the diffraction fringes from the fractal grating Cantor sets.Article Citation - WoS: 54Citation - Scopus: 55Non-Local Integrals and Derivatives on Fractal Sets With Applications(de Gruyter Open Ltd, 2016) Baleanu, D.; Golmankhaneh, Alireza K.In this paper, we discuss non-local derivatives on fractal Cantor sets. The scaling properties are given for both local and non-local fractal derivatives. The local and non-local fractal differential equations are solved and compared. Related physical models are also suggested.Article Citation - WoS: 44Citation - Scopus: 45Fractal Calculus Involving Gauge Function(Elsevier, 2016) Baleanu, Dumitru; Golmankhaneh, Alireza K.Henstock-Kurzweil integral or gauge integral is the generalization of the Riemann integral. The functions which are not integrable because of singularity in the senses of Lebesgue or Riemann are gauge integrable. In this manuscript, we have generalized F-alpha-calculus using the gauge integral method for the integrating of the functions on fractal set subset of real-line where they have singularities. The suggested new method leads to the wider class of functions on the fractal subset of real-line that are *F-alpha-integrable, Using gauge function we define *F-alpha-derivative of functions their *F-alpha-derivative is not exist. The reported results can be used for generalizing the fundamental theorem of F-alpha-calculus. (C) 2016 Elsevier B.V. All rights reserved.Article Citation - WoS: 31Citation - Scopus: 36New Derivatives on the Fractal Subset of Real-Line(Mdpi, 2016) Baleanu, Dumitru; Golmankhaneh, Alireza KhaliliIn 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.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.