Variable-Order Fractional Scale Calculus

Duarte Valério, Manuel D. Ortigueira

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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General variable-order fractional scale derivatives are introduced and studied. Both the stretching and the shrinking cases are considered for definitions of the derivatives of the GL type and of the Hadamard type. Their properties are deduced and discussed. Fractional variable-order systems of autoregressive–moving-average type are introduced and exemplified. The corresponding transfer functions are obtained and used to find the corresponding impulse responses.
Original languageEnglish
Article number4549
Number of pages13
Issue number21
Publication statusPublished - 4 Nov 2023


  • Hadamard derivative
  • logarithmic series
  • scale derivative
  • variable-order derivative


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