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Fractional Calculus and Applied Analysis

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Volume 20, Issue 4

Fractional sobolev spaces and functions of bounded variation of one variable

Maïtine Bergounioux
  • Laboratoire MAPMO, CNRS, UMR 7349 Fédération Denis Poisson, FR 2964 Université d’Orléans, B.P. 6759 45067 Orléans cedex 2, France
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/ Antonio Leaci / Giacomo Nardi / Franco Tomarelli
Published Online: 2017-08-08 | DOI: https://doi.org/10.1515/fca-2017-0049


We investigate the 1D Riemann-Liouville fractional derivative focusing on the connections with fractional Sobolev spaces, the space BV of functions of bounded variation, whose derivatives are not functions but measures and the space SBV, say the space of bounded variation functions whose derivative has no Cantor part. We prove that SBV is included in Ws,1 for every s ∈ (0, 1) while the result remains open for BV. We study examples and address open questions.

MSC 2010: Primary 26A30; Secondary 26A33; 26A45

Key Words and Phrases: fractional calculus; bounded variation functions; Riemann-Liouville derivative; Marchaud derivative; Sobolev spaces


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About the article

Received: 2016-07-27

Revised: 2017-06-20

Published Online: 2017-08-08

Published in Print: 2017-08-28

Citation Information: Fractional Calculus and Applied Analysis, Volume 20, Issue 4, Pages 936–962, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2017-0049.

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