A Hybrid Numerical Scheme for Fractional-Order Systems

  • L. L. Ferrás
  • N. J. Ford
  • M. L. MorgadoEmail author
  • M. Rebelo
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 505)


In this work we present a hybrid numerical scheme for the solution of systems of fractional differential equations arising in several fields of engineering. The numerical scheme can deal with both smooth and non-smooth solutions, and, the idea behind the hybrid method is that of approximating the solution as a linear combination of non-polynomial functions in a region near the singularity, and by polynomials in the remaining domain. The numerical method is then used to study fractional RC electrical circuits.


Fractional differential equations Caputo derivative Non-polynomial collocation method Polynomial collocation method Electrical circuits 



The first, third and fourth authors would like to thank the funding by FCT-Portuguese Foundation for Science and Technology through scholarship and projects: SFRH/BPD/100353/2014 and UID/Multi/04621/2013, UID/MAT/00297/2013 (Centro de Matemática e Aplicações), respectively.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • L. L. Ferrás
    • 1
    • 2
  • N. J. Ford
    • 2
  • M. L. Morgado
    • 3
    Email author
  • M. Rebelo
    • 4
  1. 1.Institute for Polymers and Composites/I3N & CMAT-UMUniversity of MinhoGuimarãesPortugal
  2. 2.Department of MathematicsUniversity of ChesterChesterUK
  3. 3.CEMAT, Instituto Superior Técnico, Universidade de Lisboa and Department of MathematicsUniversity of Trás-os-Montes e Alto Douro, UTADVila RealPortugal
  4. 4.Centro de Matemática e Aplicações (CMA) and Departamento de Matemática, Faculdade de Ciências e TecnologiaUniversidade NOVA de LisboaCaparicaPortugal

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