Fractional Sobolev Spaces via Riemann-Liouville Derivatives

Using Riemann-Liouville derivatives, we introduce fractional Sobolev spaces, characterize them, define 7 Piece Queen Bedroom 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 Vitamins problems is given as well.