Shifted fractional Jacobi spectral algorithm for solving distributed order time-fractional reaction–diffusion equations

  • M. A. Abdelkawy
  • António M. LopesEmail author
  • M. A. Zaky


This paper proposes a new method for solving distributed order time-fractional reaction–diffusion equations (DO-TFRDEs). Extended versions of the shifted Jacobi–Gauss–Lobatto and shifted fractional order Jacobi–Gauss–Radau collocation methods are developed for reducing the DO-TFRDEs to systems of algebraic equations and computing their approximate solutions. The applicability and accuracy of the method is illustrated through numerical examples.


Spectral collocation method Caputo fractional derivative Distributed order fractional reaction–diffusion equation 

Mathematics Subject Classification

65M70 74S25 26A33 35R11 



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© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud IslamicUniversity (IMSIU)RiyadhSaudi Arabia
  2. 2.Department of Mathematics, Faculty of ScienceBeni-Suef UniversityBeni-SuefEgypt
  3. 3.UISPA–LAETA/INEGI, Faculty of EngineeringUniversity of PortoPortoPortugal
  4. 4.Department of Applied MathematicsNational Research CentreGizaEgypt

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