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Bilateral Riemann-Liouville Fractional Sobolev spaces


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.

DOI Code: 10.1285/i15900932v41n2p61

Keywords: Fractional Calculus; Fractional Sobolev and BV Spaces

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