PROPERTIES OF THE CAPUTO-FABRIZIO FRACTIONAL DERIVATIVE AND ITS DISTRIBUTIONAL SETTINGS

被引：67

作者：

Atanackovic, Teodor M. ^{[1
]}

Pilipovic, Stevan ^{[2
]}

Zorica, Dusan ^{[3
,4
]}

机构：

[1] Univ Novi Sad, Fac Tech Sci, Trg D Obradovica 6, Novi Sad 21000, Serbia

[2] Univ Novi Sad, Fac Sci, Dept Math & Informat, Trg D Obradovica 4, Novi Sad 21000, Serbia

[3] Serbian Acad Arts & Sci, Math Inst, Kneza Mihaila 36, Beograd 11000, Serbia

[4] Univ Novi Sad, Dept Phys, Fac Sci, Trg D Obradovica 4, Novi Sad 21000, Serbia

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2018年 / 21卷 / 01期

关键词：

Caputo-Fabrizio fractional derivative; variational calculus; linear viscoelasticity; DIFFERENTIAL-EQUATIONS; EULER-LAGRANGE; FORMULATION;

D O I：

10.1515/fca-2018-0003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：29 / 44

页数：16

共 27 条

[11] Dissipativity and stability for a nonlinear differential equation with distributed order symmetrized fractional derivative [J].

Atanackovic, Teodor M. ;

Dolicanin, Diana ;

Konjik, Sanja ;

Pilipovic, Stevan .

APPLIED MATHEMATICS LETTERS, 2011, 24 (06) :1020-1025

[12] A new method for investigating approximate solutions of some fractional integro-differential equations involving the Caputo-Fabrizio derivative [J].

Baleanu, Dumitru ;

Mousalou, Asef ;

Rezapour, Shahram .

ADVANCES IN DIFFERENCE EQUATIONS, 2017,

[13]

Caputo M., 2015, Progress Fract. Diff. Appl, V1, P73, DOI DOI 10.12785/PFDA/010201

[14] On the notion of fractional derivative and applications to the hysteresis phenomena [J].

Caputo, Michele ;

Fabrizio, Mauro .

MECCANICA, 2017, 52 (13) :3043-3052

[15] Formulation of Euler-Lagrange and Hamilton equations involving fractional operators with regular kernel [J].

Coronel-Escamilla, Antonio ;

Francisco Gomez-Aguilar, Jose ;

Baleanu, Dumitru ;

Fabricio Escobar-Jimenez, Ricardo ;

Hugo Olivares-Peregrino, Victor ;

Abundez-Pliego, Arturo .

ADVANCES IN DIFFERENCE EQUATIONS, 2016,

[16]

Diethelm K., 2010, LECT NOTES MATH

[17] ON A NEW CLASS OF CONSTITUTIVE EQUATIONS FOR LINEAR VISCOELASTIC BODY [J].

Dolicanin-Dekic, Diana .

FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2017, 20 (02) :521-536

[18]

Gelfand I. M., 2000, Calculus of variations

[19]

Kiryakova V., 1994, Generalized fractional calculus and applications, V301

[20] The special functions of fractional calculus as generalized fractional calculus operators of some basic functions [J].

Kiryakova, Virginia .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (03) :1128-1141

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