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.Q4Subject: search.filters.subject.Caputo Derivatives

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  • Article
    Citation - WoS: 66
    Citation - Scopus: 63
    An Accurate Numerical Technique for Solving Fractional Optimal Control Problems
    (Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.; Abdelkawy, M. A.; Matematik
    In this article, we propose the shifted Legendre orthonormal polynomials for the numerical solution of the fractional optimal control problems that appear in several branches of physics and engineering. The Rayleigh-Ritz method for the necessary conditions of optimization and the operational matrix of fractional derivatives are used together with the help of the properties of the shifted Legendre orthonormal polynomials to reduce the fractional optimal control problem to solving a system of algebraic equations that greatly simplifies the problem. For confirming the efficiency and accuracy of the proposed technique, an illustrative numerical example is introduced with its approximate solution.
  • Article
    Citation - WoS: 26
    A Chebyshev-Laguerre Collocation Scheme for Solving A Time Fractional Sub-Diffusion Equation on A Semi-Infinite Domain
    (Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Abdelkawy, M. A.; Alzahrani, A. A.; Baleanu, D.; Alzahrani, E. O.; Matematik
    We propose a new efficient spectral collocation method for solving a time fractional sub-diffusion equation on a semi-infinite domain. The shifted Chebyshev-Gauss-Radau interpolation method is adapted for time discretization along with the Laguerre-Gauss-Radau collocation scheme that is used for space discretization on a semi-infinite domain. The main advantage of the proposed approach is that a spectral method is implemented for both time and space discretizations, which allows us to present a new efficient algorithm for solving time fractional sub-diffusion equations.