We establish some properties of the bilateral Riemann–Liouville fractional derivative Ds. 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
Tomarelli, Franco
2022-01-01
Abstract
We establish some properties of the bilateral Riemann–Liouville fractional derivative Ds. 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:
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