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Fractional Chebyshev Collocation Method for Solving Linear Fractional-Order Delay-Differential Equations

[+] Author Affiliations
Arman Dabiri, Eric A. Butcher

University of Arizona, Tucson, AZ

Paper No. DETC2017-68333, pp. V006T10A066; 9 pages
  • ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 13th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Cleveland, Ohio, USA, August 6–9, 2017
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5820-2
  • Copyright © 2017 by ASME


An efficient numerical method, the fractional Chebyshev collocation method, is proposed for obtaining the solution of a system of linear fractional order delay-differential equations (FDDEs). It is shown that the proposed method overcomes several limitations of current numerical methods for solving linear FDDEs. For instance, the proposed method can be used for linear incommensurate order fractional differential equations and FDDEs, has spectral convergence (unlike finite differences), and does not require a canonical form. To accomplish this, a fractional differentiation matrix is derived at the Chebyshev-Gauss-Lobatto collocation points by using the discrete orthogonal relationship of the Chebyshev polynomials. Then, using two proposed discretization operators for matrix functions results in an explicit form of solution for a system of linear FDDEs with discrete delays. The advantages of using the fractional Chebyshev collocation method are demonstrated in two numerical examples in which the proposed method is compared with the Adams-Bashforth-Moulton method.

Copyright © 2017 by ASME



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