We establish some properties of the bilateral Riemann–Liouville fractional derivative $D^s$. We set the notation, and study the associated Sobolev spaces of fractional order s, denoted by $W^{s,1}(a, b)$, and the fractional bounded variation spaces of fractional order s, denoted by $BV^s(a, b)$. Examples, embeddings and compactness properties related to these spaces are addressed, aiming to set a functional framework suitable for fractional variational models for image analysis.
Riemann–Liouville Fractional Sobolev and Bounded Variation Spaces
Antonio Leaci
;Franco Tomarelli
2022-01-01
Abstract
We establish some properties of the bilateral Riemann–Liouville fractional derivative $D^s$. We set the notation, and study the associated Sobolev spaces of fractional order s, denoted by $W^{s,1}(a, b)$, and the fractional bounded variation spaces of fractional order s, denoted by $BV^s(a, b)$. Examples, embeddings and compactness properties related to these spaces are addressed, aiming to set a functional framework suitable for fractional variational models for image analysis.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
