Riemann–Liouville Fractional Sobolev and Bounded Variation Spaces - Antonio Leaci; Franco Tomarelli (Axioms, 2022)
We establish some properties of the bilateral Riemann–Liouville fractional derivative <semantics>Ds</semantics>. We set the notation, and study the associated Sobolev spaces of fractional order s, denoted by <semantics>Ws,1(a,b)</semantics>, and the fractional bounded variation spaces of fractional order s, denoted by <semantics>BVs(a,b)</semantics>. 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.