WoS İndeksli Yayınlar Koleksiyonu

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

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Scopus Q: search.filters.scopusQuartile.Q3Subject: search.filters.subject.Operational Matrix

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  • Article
    Citation - WoS: 29
    Citation - Scopus: 31
    A Novel Spectral Approximation for the Two-Dimensional Fractional Sub-Diffusion Problems
    (Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Zaky, M. A.; Baleanu, D.; Abdelkawy, M. A.; Matematik
    This paper reports a new numerical method that enables easy and convenient discretization of a two-dimensional sub-diffusion equation with fractional derivatives of any order. The suggested method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional derivatives, described in the Caputo sense. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. The validity and effectiveness of the method are demonstrated by solving two numerical examples, which are presented in the form of tables and graphs to make more easier comparisons with the exact solutions and the results obtained by other methods.
  • Article
    Citation - WoS: 44
    Citation - Scopus: 52
    New Numerical Approach for Fractional Variational Problems Using Shifted Legendre Orthonormal Polynomials
    (Springer/plenum Publishers, 2017) Hafez, Ramy M.; Bhrawy, Ali H.; Baleanu, Dumitru; El-Kalaawy, Ahmed A.; Ezz-Eldien, Samer S.
    This paper reports a new numerical approach for numerically solving types of fractional variational problems. In our approach, we use the fractional integrals operational matrix, described in the sense of Riemann-Liouville, with the help of the Lagrange multiplier technique for converting the fractional variational problem into an easier problem that consisting of solving an algebraic equations system in the unknown coefficients. Several numerical examples are introduced, combined with their approximate solutions and comparisons with other numerical approaches, for confirming the accuracy and applicability of the proposed approach.