Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Publisher: search.filters.publisher.Academic Press inc Elsevier ScienceSubject: search.filters.subject.Caputo Derivative

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  • Article
    Citation - WoS: 67
    Citation - Scopus: 70
    Numerical Approximation of Higher-Order Time-Fractional Telegraph Equation by Using a Combination of a Geometric Approach and Method of Line
    (Academic Press inc Elsevier Science, 2016) Baleanu, D.; Hashemi, M. S.
    We propose a simple and accurate numerical scheme for solving the time fractional telegraph (TFT) equation within Caputo type fractional derivative. A fictitious coordinate v is imposed onto the problem in order to transform the dependent variable u(x, t) into a new variable with an extra dimension. In the new space with the added fictitious dimension, a combination of method of line and group preserving scheme (GPS) is proposed to find the approximate solutions. This method preserves the geometric structure of the problem. Power and accuracy of this method has been illustrated through some examples of TFT equation. (C) 2016 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 203
    Citation - Scopus: 217
    A Spectral Tau Algorithm Based on Jacobi Operational Matrix for Numerical Solution of Time Fractional Diffusion-Wave Equations
    (Academic Press inc Elsevier Science, 2015) Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.; Bhrawy, A. H.
    In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann-Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The validity and effectiveness of the method are demonstrated by solving five numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier. (C) 2014 Elsevier Inc. All rights reserved.