On a New Symmetric Fractional Variable Order Derivative

被引：10

作者：

Sierociuk, Dominik ^{[1
]}

Malesza, Wiktor ^{[1
]}

Macias, Michal ^{[1
]}

机构：

[1] Warsaw Univ Technol, Inst Control & Ind Elect, Koszykowa 75, PL-00662 Warsaw, Poland

来源：

THEORETICAL DEVELOPMENTS AND APPLICATIONS OF NON-INTEGER ORDER SYSTEMS | 2016年 / 357卷

关键词：

Fractional calculus; Variable order derivative;

D O I：

10.1007/978-3-319-23039-9_3

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The paper presents particular definitions of symmetric fractional variable order derivatives. The.. and.. types of the fractional variable order derivatives and their properties have been introduced. Additionally, the switching order schemes equivalent to these types of definitions have been shown. Finally, the theoretical considerations have been validated on numerical examples.

引用

页码：29 / 39

页数：11

共 18 条

[1]

Chien-Cheng Tseng, 2011, 2011 European Conference on Circuit Theory and Design (ECCTD 2011), P17, DOI 10.1109/ECCTD.2011.6043299

[2] Comparison and validation of integer and fractional order ultracapacitor models [J].

Dzielinski, Andrzej ;

Sarwas, Grzegorz ;

Sierociuk, Dominik .

ADVANCES IN DIFFERENCE EQUATIONS, 2011,

[3] Variable order and distributed order fractional operators [J].

Lorenzo, CF ;

Hartley, TT .

NONLINEAR DYNAMICS, 2002, 29 (1-4) :57-98

[4]

Macias M, 2014, I C FRACTIONAL DIFF, DOI 10.1109/ICFDA.2014.6967452

[5]

Macias M, 2013, PROCEEDINGS OF THE 2013 14TH INTERNATIONAL CARPATHIAN CONTROL CONFERENCE (ICCC), P222

[6]

Podlubny I, 2000, Fract. Calc. Appl. Anal, V3, P359, DOI DOI 10.1016/J.JCP.2009.01.014)

[7] Matrix approach to discrete fractional calculus II: Partial fractional differential equations [J].

Podlubny, Igor ;

Chechkin, Aleksei ;

Skovranek, Tomas ;

Chen, YangQuan ;

Vinagre Jara, Blas M. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 228 (08) :3137-3153

[8] On the Selection and Meaning of Variable Order Operators for Dynamic Modeling [J].

Ramirez, Lynnette E. S. ;

Coimbra, Carlos F. M. .

INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 2010

[9]

Sheng H, 2010, P 4 IFAC WORKSH DIFF

[10] Duality of variable fractional order difference operators and its application in identification [J].

Sierociuk, D. ;

Twardy, M. .

BULLETIN OF THE POLISH ACADEMY OF SCIENCES-TECHNICAL SCIENCES, 2014, 62 (04) :809-815

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