Discrete-Time Fractional Difference Calculus: Origins, Evolutions, and New Formalisms

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Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types are presented, namely: nabla and delta, bilateral, tempered, bilinear, stretching, and shrinking. Both continuous and discrete-time differences are described. ARMA-type systems based on differencers are introduced and exemplified. In passing, the incorrectness of the usual delta difference is shown.
Original languageEnglish
Article number502
Number of pages32
JournalFractal and Fractional
Issue number7
Publication statusPublished - 25 Jun 2023


  • ARMA
  • bilateral difference
  • bilinear
  • delta difference
  • nabla difference
  • stretching difference
  • tempered


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