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Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Subject: search.filters.subject.Cantor Set

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Now showing 1 - 6 of 6
  • Article
    Citation - WoS: 37
    Citation - Scopus: 38
    Newtonian Mechanics on Fractals Subset of Real-Line
    (Editura Acad Romane, 2013) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Fazlollahi, Vahideh; Baleanu, Dumitru; Matematik
    In this paper, we have studied the calculus on the fractals, meanwhile Newtonian mechanics on fractals subset of real-line has been suggested. Further, work and energy theorem on fractals with the examples has been explained. Finally Langevin F-alpha-Equation on fractals is derived.
  • Article
    Citation - WoS: 102
    Citation - Scopus: 124
    Local Fractional Variational Iteration Method for Diffusion and Wave Equations on Cantor Sets
    (Editura Acad Romane, 2014) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Khan, Yasir; Mohyud-Din, S. T.; Matematik
    In this work, the local fractional variational iteration method is employed to handle the sub-diffusion and wave equations and the analytical solutions are obtained. The present method is efficient and implicit to investigate the differential equations with the local fractional derivatives.
  • Article
    Citation - WoS: 148
    Citation - Scopus: 155
    Cantor-Type Cylindrical-Coordinate Method for Differential Equations With Local Fractional Derivatives
    (Elsevier Science Bv, 2013) Srivastava, H. M.; He, Ji-Huan; Baleanu, Dumitru; Yang, Xiao-Jun
    In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems. (c) 2013 Published by Elsevier B.V.
  • Article
    Citation - WoS: 21
    Citation - Scopus: 34
    New Relationships Connecting a Class of Fractal Objects and Fractional Integrals in Space
    (versita, 2013) Baleanu, Dumitru; Nigmatullin, Raoul R.
    Many specialists working in the field of the fractional calculus and its applications simply replace the integer differentiation and integration operators by their non-integer generalizations and do not give any serious justifications for this replacement. What kind of "Physics" lies in this mathematical replacement? Is it possible to justify this replacement or not for the given type of fractal and find the proper physical meaning? These or other similar questions are not discussed properly in the current papers related to this subject. In this paper new approach that relates to the procedure of the averaging of smooth functions on a fractal set with fractional integrals is suggested. This approach contains the previous one as a partial case and gives new solutions when the microscopic function entering into the structural-factor does not have finite value at N a parts per thousand << 1 (N is number of self-similar objects). The approach was tested on the spatial Cantor set having M bars with different symmetry. There are cases when the averaging procedure leads to the power-law exponent that does not coincide with the fractal dimension of the self-similar object averaged. These new results will help researches to understand more clearly the meaning of the fractional integral. The limits of applicability of this approach and class of fractal are specified.
  • Article
    Citation - WoS: 17
    Citation - Scopus: 16
    On Local Fractional Operators View of Computational Complexity Diffusion and Relaxation Defined on Cantor Sets
    (Vinca inst Nuclear Sci, 2016) Zhang, Zhi-Zhen; Machado, J. A. Tenreiro; Yang, Xiao-Jun; Baleanu, Dumitru
    This paper treats the description of non-differentiable dynamics occurring in complex systems governed by local fractional partial differential equations. The exact solutions of diffusion and relaxation equations with Mittag-Leffler and exponential decay defined on Cantor sets are calculated. Comparative results with other versions of the local fractional derivatives are discussed.
  • Article
    Citation - WoS: 54
    Citation - Scopus: 55
    Non-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.