An alternative definition of the fractional in space derivatives
Abstract Starting from some general considerations about the current definitions of the fractional Laplacian operator, in this work we present an alternative definition of the fractional in space derivative. The analysis exploits the theory of the operational calculus for unbounded operators with spectrum contained in the imaginary axis. The resulting operator interpolates the derivatives of arbitrary integer order.
Authors
- Paolo Novati (ORCID: https://orcid.org/0000-0002-6887-7429)
- Eleonora Denich (ORCID: https://orcid.org/0000-0003-2403-753X)
Institutions
- University of Trieste (IT)
Publication Details
- Journal
- Fractional Calculus and Applied Analysis
- Published
- 2026-07-24
- DOI
- https://doi.org/10.1007/s13540-026-00561-2
- Primary Topic
- Fractional Differential Equations Solutions
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Regione Autonoma Friuli Venezia Giulia
- Università degli Studi di Trieste
- Gruppo Nazionale per il Calcolo Scientifico