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Journal of Function Spaces and Applications
Volume 2013, Article ID 128043, 15 pages
Research Article

Fractional Sobolev Spaces via Riemann-Liouville Derivatives

Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland

Received 31 July 2013; Accepted 19 October 2013

Academic Editor: Ismat Beg

Copyright © 2013 Dariusz Idczak and Stanisław Walczak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.