Numerical solution of multi-order fractional differential equations with multiple delays via spectral collocation methods

Arman Dabiri, Eric Butcher

Research output: Contribution to journalArticle

30 Scopus citations


This paper discusses a general framework for the numerical solution of multi-order fractional delay differential equations (FDDEs) in noncanonical forms with irrational/rational multiple delays by the use of a spectral collocation method. In contrast to the current numerical methods for solving fractional differential equations, the proposed framework can solve multi-order FDDEs in a noncanonical form with incommensurate orders. The framework can also solve multi-order FDDEs with irrational multiple delays. Next, the framework is enhanced by the fractional Chebyshev collocation method in which a Chebyshev operation matrix is constructed for the fractional differentiation. Spectral convergence and small computational time are two other advantages of the proposed framework enhanced by the fractional Chebyshev collocation method. In addition, the convergence, error estimates, and numerical stability of the proposed framework for solving FDDEs are studied. The advantages and computational implications of the proposed framework are discussed and verified in several numerical examples.

Original languageEnglish (US)
Pages (from-to)424-448
Number of pages25
JournalApplied Mathematical Modelling
Publication statusPublished - Apr 1 2018



  • Convergence and error estimates
  • Delay differential equation
  • Multi-order fractional differential equation
  • Numerical method
  • Numerical stability
  • Spectral method

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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