Properties of the Caputo-Fabrizio fractional derivative and its distributional settings-Reference-Cited by-同舟云学术

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

Published:2018-02-01 Issue:1 Volume:21 Page:29-44
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Atanacković Teodor M.¹,Pilipović Stevan²,Zorica Dušan³⁴

Affiliation:

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

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

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

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

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2018-0003/pdf

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