Recursive-operational method for fractional systems: System theory without Laplace transform

Gabriel Bengochea, Manuel Ortigueira, Luis Verde-Star, António Mendes Lopes

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


In this chapter we present a recursive-operational method for studying fractional continuous-time linear systems. The approach that we follow is an algebraic version of the usual convolution product. With it, we are able to compute the output of fractional linear systems. The method is recursive in the sense that we can add or remove (pseudo-) poles or zeros individually. The performance and accuracy of the method are illustrated by numerical examples. The procedure can be used also in nonlinear systems. To illustrate this feature we solve the fractional version of the logistic equation.

Original languageEnglish
Title of host publicationApplications in Engineering, Life and Social Sciences, Part B
PublisherDe Gruyter
Number of pages29
ISBN (Electronic)9783110571929
ISBN (Print)9783110570922
Publication statusPublished - 1 Jan 2019


  • Fractional derivative
  • Fractional systems
  • Operational calculus


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