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Substantial, Tempered, and Shifted Fractional Derivatives: Three Faces of a Tetrahedron
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  • Manuel Ortigueira,
  • Gabriel BengocheaOrcid,
  • José Tenreiro MACHADOOrcid
Manuel Ortigueira
Faculty of Sciences and Technology of Universidade Nova de Lisboa, Universidade Nova de Lisboa
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Gabriel Bengochea
Orcid
Universidad Autónoma de la Ciudad de México
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José Tenreiro MACHADO
Orcid
Institute of Engineering, Polytechnic of Porto
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Peer review status:UNDER REVIEW

31 May 2020Submitted to Mathematical Methods in the Applied Sciences
05 Jun 2020Assigned to Editor
05 Jun 2020Submission Checks Completed
08 Jun 2020Reviewer(s) Assigned

Abstract

The substantial, tempered, and shifted fractional derivatives are introduced in a unified framework. Their properties are studied and, in the light of the strict sense criterion for derivative definitions, they are characterized and assessed. In the scope of the framework, new tempered linear sytems and transfer functions are introduced.