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

Reference27 articles.

1. R. Adams, J.J.F. Fournier, Sobolev Spaces. Elsevier, Oxford (2003).

2. O.P. Agrawal, Formulation of Euler-Lagrange equations for fractional variational problems. J. Math. Anal. Appl.272 (2002), 368–79.

3. T.M. Atanackovic, D. Dolicanin, S. Konjik, S. Pilipovic, Dissipativity and stability for a nonlinear differential equation with distributed order symmetrized fractional derivative. Appl. Math. Lett.24 (2011), 1020–1025.

4. T.M. Atanackovic, B. Stankovic, On a numerical scheme for solving differential equations of fractional order. Mech. Res. Commun.35 (2008), 429–438.

5. T.M. Atanackovic, M. Janev, S. Konjik, S. Pilipovic, D. Zorica, Expansion formula for fractional derivatives in variational problems. J. Math. Anal. Appl.409 (2014), 911–924.

Cited by 67 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On some properties of generalized cardinal sine kernel fractional operators: Advantages and applications of the extended operators;Chinese Journal of Physics;2024-10

2. Fractional calculus for distributions;Fractional Calculus and Applied Analysis;2024-08-29

3. On analysis of a system of non-homogenous boundary value problems using hausdorff derivative with exponential kernel;Journal of Applied Mathematics and Computing;2024-07-31

4. Theoretical and computational results for implicit non-singular hybrid fractional differential equation subject to multi-terms non-local initial conditions;Journal of Mathematics and Computer Science;2024-07-15

5. Comparison of unsteady MHD flow of second grade fluid by two fractional derivatives;Numerical Heat Transfer, Part A: Applications;2024-07-08