|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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