Fractional Sobolev Spaces via Riemann-Liouville Derivatives

摘要

Using Riemann-Liouville derivatives, we introduce fractional Sobolevspaces, characterize them, define weak fractional derivatives, and show that they coincide with the Riemann-Liouville ones. Next, weprove equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, separability, and compactness ofsome imbeddings. An application to boundary value problems is given as well.