We establish some notation and properties of the bilateral Riemann-Liouville fractional derivative $D^s$. We introduce the associated Sobolev spaces of fractional order s, denoted by $W^{s,1}(a, b)$, and the Bounded Variation spaces of fractional order s, denoted by $BV^s(a, b)$: these spaces are studied with the aim of providing a suitable functional framework for fractional variational models in image analysis.
Bilateral Riemann-Liouville Fractional Sobolev spaces
Antonio Leaci
;Franco Tomarelli
2021-01-01
Abstract
We establish some notation and properties of the bilateral Riemann-Liouville fractional derivative $D^s$. We introduce the associated Sobolev spaces of fractional order s, denoted by $W^{s,1}(a, b)$, and the Bounded Variation spaces of fractional order s, denoted by $BV^s(a, b)$: these spaces are studied with the aim of providing a suitable functional framework for fractional variational models in image analysis.File in questo prodotto:
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