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Properties of the Caputo-Fabrizio fractional derivative and its distributional settings

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Abstract

The Caputo-Fabrizio fractional derivative is analyzed in classical and distributional settings. The integral inequalities needed for application in linear viscoelasticity are presented. They are obtained from the entropy inequality in a weak form. Moreover, integration by parts, an expansion formula, approximation formula and generalized variational principles of Hamilton’s type are given. Hamilton’s action integral in the first principle, do not coincide with the lower bound in the fractional integral, while in the second principle the minimization is performed with respect to a function from a specified space and the order of fractional derivative.

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Authors and Affiliations

  1. Faculty of Technical Sciences, University of Novi Sad, “Trg D. Obradovića”, 6, Novi Sad, 21000, Serbia

    Teodor M. Atanacković

  2. Department of Mathematics and Informatics Faculty of Sciences, University of Novi Sad, “Trg D. Obradovića”, 4, Novi Sad, 21000, Serbia

    Stevan Pilipović

  3. Mathematical Institute, Serbian Academy of Arts and Sciences, “Kneza Mihaila”, 36, Beograd, 11000, Serbia

    Dušan Zorica

  4. Department of Physics, Faculty of Sciences, University of Novi Sad, “Trg D. Obradovića”, 4, Novi Sad, 21000, Serbia

    Dušan Zorica

Authors
  1. Teodor M. Atanacković
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  2. Stevan Pilipović
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  3. Dušan Zorica
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Correspondence to Teodor M. Atanacković.

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Atanacković, T.M., Pilipović, S. & Zorica, D. Properties of the Caputo-Fabrizio fractional derivative and its distributional settings. FCAA 21, 29–44 (2018). https://doi.org/10.1515/fca-2018-0003

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  • DOI: https://doi.org/10.1515/fca-2018-0003

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