Fractional Scale Calculus: Hadamard vs. Liouville

Manuel D. Ortigueira, Gary W. Bohannan

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
19 Downloads (Pure)


A general fractional scale derivative is introduced and studied. Its relation with the Hadamard derivatives is established and reformulated. A new derivative similar to the Grünwald–Letnikov’s is deduced. Tempered versions are also introduced. Scale-invariant systems are described and exemplified. For solving the corresponding differential equations, a new logarithmic Mittag-Leffler series is proposed.

Original languageEnglish
Article number296
Number of pages19
JournalFractal and Fractional
Issue number4
Publication statusPublished - Apr 2023


  • Hadamard derivative
  • Liouville derivative
  • logarithmic series
  • scale derivative
  • tempered derivative


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