WoS İndeksli Yayınlar Koleksiyonu

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

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Publisher: search.filters.publisher.Vinca inst Nuclear SciSubject: search.filters.subject.Local Fractional Derivative

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Now showing 1 - 3 of 3
  • 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.
  • Conference Object
    Citation - WoS: 16
    Citation - Scopus: 16
    Observing Diffusion Problems Defined on Cantor Sets in Different Co-Ordinate Systems
    (Vinca inst Nuclear Sci, 2015) Baleanu, Dumitru; Baleanu, Mihaela-Cristina; Yang, Xiao-Jun
    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.
  • Conference Object
    Citation - WoS: 16
    Citation - Scopus: 15
    A New Numerical Technique for Solving Fractional Sub-Diffusion and Reaction Sub-Diffusion Equations With A Non-Linear Source Term
    (Vinca inst Nuclear Sci, 2015) Baleanu, Dumitru; Mallawi, Fouad; Bhrawy, Ali H.
    In this paper, we are concerned with the fractional sub-diffusion equation with a non-linear source term. The Legendre spectral collocation method is introduced together with the operational matrix of fractional derivatives (described in the Caputo sense) to solve the fractional sub-diffusion equation with a non-linear source term. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem. In addition, the Legendre spectral collocation methods applied also for a solution of the fractional reaction sub-diffusion equation with a non-linear source term. For confirming the validity and accuracy of the numerical scheme proposed, two numerical examples with their approximate solutions are presented with comparisons between our numerical results and those obtained by other methods.