Fractional Sobolev spaces via Riemann-Liouville derivatives

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. © 2013 dariusz idczak and stanisław walczak.