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,W-1(a, b), and the Bounded Variation spaces of fractional order s, denoted by BVs(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

Tomarelli, F
2021

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,W-1(a, b), and the Bounded Variation spaces of fractional order s, denoted by BVs(a, b): these spaces are studied with the aim of providing a suitable functional framework for fractional variational models in image analysis.
Fractional Calculus
Fractional Sobolev and BV Spaces
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1193813
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