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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11587/459597
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