Browsing by Author "Baleanu, Mihaela Cristina"

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Fractional Electromagnetic Equations Using Fractional Forms
(Springer/Plenum Publishers, 2009) Baleanu, Dumitru; Golmankhaneh, Ali K.; Golmankhaneh, Alireza K.; Baleanu, Mihaela Cristina
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
Fractional odd-dimensional mechanics
(Springer International Publishing, 2011) Baleanu, Dumitru; Golmankhaneh, Alireza K.; Baleanu, Dumitru; Baleanu, Mihaela Cristina
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
Hamiltonian structure of fractional first order lagrangian
(Springer/Plenum Publishers, 2010) Baleanu, Dumitru; Golmankhaneh, Alireza K.; Baleanu, Dumitru; Baleanu, Mihaela Cristina
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
Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators
(Hindawi LTD, 2014) Baleanu, Dumitru; Tenreiro Machado, J. A.; Cattani, Carlo; Baleanu, Mihaela Cristina; Yang, Xiao-Jun; 56389
We perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.
Mappings for Special Functions on Cantor Sets and Special Integral Transforms via Local Fractional Operators
(Hindawi LTD, 2013) Baleanu, Dumitru; Baleanu, Dumitru; Baleanu, Mihaela Cristina; Cheng, De-Fu; Yang, Xiao-Jun; 56389
The mappings for some special functions on Cantor sets are investigated. Meanwhile, we apply the local fractional Fourier series, Fourier transforms, and Laplace transforms to solve three local fractional differential equations, and the corresponding nondifferentiable solutions were presented.
Multidimensional Scaling for Orthodontic Root Resorption
(Hindawi LTD, 2013) Baleanu, Dumitru; Lonescu, Ecaterina; Preoteasa, Elena; Tenreiro Machado, J. A.; Baleanu, Mihaela Cristina; Baleanu, Dumitru; 56389
The paper investigates the risk factors for the severity of orthodontic root resorption. The multidimensional scaling (MDS) visualization method is used to investigate the experimental data from patients who received orthodontic treatment at the Department of Orthodontics and Dentofacial Orthopedics, Faculty of Dentistry, "Carol Davila" University of Medicine and Pharmacy, during a period of 4 years. The clusters emerging in the MDS plots reveal features and properties not easily captured by classical statistical tools. The results support the adoption of MDS for tackling the dentistry information and overcoming noise embedded into the data. The method introduced in this paper is rapid, efficient, and very useful for treating the risk factors for the severity of orthodontic root resorption.
Observing diffusion problems defined on cantor sets in different co-ordinate systems
(Vinca Inst Nuclear Sci., 2015) Baleanu, Dumitru; Baleanu, Dumitru; Baleanu, Mihaela Cristina
In this paper, the 2-D and 3-D diffusions defined on Cantor sets with local fractional differential operator were discussed in different co-ordinate systems. The 2-D diffusion in Cantorian co-ordinate system can be converted into the symmetric diffusion defined on Cantor sets. The 3-D diffusions in Cantorian co-ordinate system can be observed in the Cantor-type cylindrical and spherical co-ordinate methods.