Fractional Sobolev Spaces via Riemann-Liouville Derivatives. (8th December 2013) - Idczak, Dariusz; Walczak, Stanisław
Abstract : Using Riemann-Liouville derivatives, we introduce fractional Sobolev spaces, characterize them, define weak fractional derivatives, and show that they coincide with the Riemann-Liouville ones. Next, we prove equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, separability, and compactness of some imbeddings. An application to boundary value problems is given as well.