On fractional-Legendre spectral Galerkin method for fractional Sturm–Liouville problems

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41 Citations (Scopus)


In this paper, we present a numerical technique for solving fractional Sturm–Liouville problems with variable coefficients subject to mixed boundary conditions. The proposed algorithm is a spectral Galerkin method based on fractional-order Legendre functions. Tedious manipulation of the series appearing in the implementation of the method have been carried out to obtain a system of algebraic equations for the coefficients. Our findings demonstrate the possibility of having no eigenvalues, finite number of eigenvalues or infinite number of eigenvalues depending on the fractional order. The convergence and effectiveness of the present algorithm are demonstrated through several numerical examples.

Original languageEnglish
Pages (from-to)261-267
Number of pages7
JournalChaos, Solitons and Fractals
Publication statusPublished - Nov 2018


  • Caputo derivative
  • Eigenvalues and eigenfunctions
  • Fractional Legendre functions
  • Fractional Sturm–Liouville problems
  • Spectral methods

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics
  • General Physics and Astronomy
  • Mathematical Physics


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