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

Peer review status:Published

31 May 2020Submitted to Mathematical Methods in the Applied Sciences
05 Jun 2020Submission Checks Completed
05 Jun 2020Assigned to Editor
08 Jun 2020Reviewer(s) Assigned
31 Oct 2020Review(s) Completed, Editorial Evaluation Pending
02 Nov 2020Editorial Decision: Revise Major
04 Nov 20201st Revision Received
05 Nov 2020Assigned to Editor
05 Nov 2020Submission Checks Completed
05 Nov 2020Reviewer(s) Assigned
05 Nov 2020Review(s) Completed, Editorial Evaluation Pending
07 Nov 2020Editorial Decision: Accept
04 Dec 20202nd Revision Received
04 Dec 2020Submission Checks Completed
04 Dec 2020Assigned to Editor
11 Dec 2020Reviewer(s) Assigned
11 Feb 2021Review(s) Completed, Editorial Evaluation Pending
15 Feb 2021Editorial Decision: Revise Minor
16 Feb 20213rd Revision Received
16 Feb 2021Assigned to Editor
16 Feb 2021Submission Checks Completed
16 Feb 2021Editorial Decision: Accept
07 Apr 2021Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.7343