Rhapsody in fractional

Jose Tenreiro Machado, António Mendes Lopes, Fernando B.M. Duarte, Manuel Duarte Ortigueira, Raul Tello Rato

Research output: Contribution to journalArticle

29 Citations (Scopus)


This paper studies several topics related with the concept of “frac- tional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabil- ities, fractional delay discrete-time linear systems, and fractional Fourier transform.
Original languageEnglish
Pages (from-to)1188-1214
JournalFractional Calculus and Applied Analysis
Issue number4
Publication statusPublished - 2014


  • difference equations
  • fractional delay
  • fractional Fourier transform
  • fractional sums
  • matrix power
  • matrix root
  • negative probability
  • positional number systems
  • tolerant computing

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    Machado, J. T., Lopes, A. M., Duarte, F. B. M., Ortigueira, M. D., & Rato, R. T. (2014). Rhapsody in fractional. Fractional Calculus and Applied Analysis, 17(4), 1188-1214. https://doi.org/10.2478/s13540-014-0206-0