Authors: Atanacković, Teodor
Pilipović, Stevan
Zorica, Dušan 
Title: Properties of the Caputo-Fabrizio fractional derivative and its distributional settings
Journal: Fractional Calculus and Applied Analysis
Volume: 21
Issue: 1
First page: 29
Last page: 44
Issue Date: 23-Feb-2018
Rank: M21a
ISSN: 1311-0454
DOI: 10.1515/fca-2018-0003
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.
Keywords: Caputo-Fabrizio fractional derivative | linear viscoelasticity | variational calculus
Publisher: De Gruyter
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 
Methods of Functional and Harmonic Analysis and PDE with Singularities 

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