WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

Browse

Filters

2013 - 20163

Settings

COAR Access Rights: search.filters.coarAccessRights.open accessSubject: search.filters.subject.Fractal Calculus

Search Results

Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 14
    Citation - Scopus: 25
    On 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: 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.
  • Article
    Citation - WoS: 31
    Citation - Scopus: 36
    New Derivatives on the Fractal Subset of Real-Line
    (Mdpi, 2016) Baleanu, Dumitru; Golmankhaneh, Alireza Khalili
    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.