Fractional-order Legendre-collocation method for solving fractional initial value problems

Qasem M. Al-Mdallal, Ahmed S. Abu Omer

Research output: Contribution to journalArticlepeer-review

46 Citations (Scopus)


In this paper, we present a numerical algorithm for solving second-order fractional initial value problems. This numerical algorithm is based on a fractional Legendre-collocation spectral method. The governing fractional differential equation is converted into a nonlinear system of algebraic equations. The error analysis of the proposed numerical algorithm is presented. Comparisons with other numerical methods shows that the proposed algorithm is more accurate and simpler to implement. Several examples are discussed to illustrate the efficiency and accuracy of the present scheme.

Original languageEnglish
Pages (from-to)74-84
Number of pages11
JournalApplied Mathematics and Computation
Publication statusPublished - Mar 15 2018


  • Caputo derivative
  • Collocation method
  • Fractional Legendre functions
  • Spectral methods

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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