Caputo-Hadamard Fractional Derivatives of Variable Order

被引：45

作者：

Almeida, Ricardo ^{[1
]}

机构：

[1] Univ Aveiro, Dept Math, Ctr Res & Dev Math Applicat CIDMA, P-3810193 Aveiro, Portugal

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2017年 / 38卷 / 01期

关键词：

Caputo fractional derivative; expansion formulas; fractional calculus; Hadamard fractional derivative; variable fractional order; 26A33; 33F05; DIFFERENTIAL-OPERATORS; APPROXIMATIONS;

D O I：

10.1080/01630563.2016.1217880

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we present three types of Caputo-Hadamard derivatives of variable fractional order and study the relations between them. An approximation formula for each fractional operator, using integer-order derivatives only, is obtained and an estimation for the error is given. At the end, we compare the exact fractional derivative of a concrete example with some numerical approximations.

引用

页码：1 / 19

页数：19

共 17 条

[1]

[Anonymous], 1993, INTRO FRACTIONAL CA

[2] An expansion formula for fractional derivatives of variable order [J].

Atanackovic, Teodor M. ;

Janev, Marko ;

Pilipovic, Stevan ;

Zorica, Dusan .

CENTRAL EUROPEAN JOURNAL OF PHYSICS, 2013, 11 (10) :1350-1360

[3] Stirling functions of the second kind in the setting of difference and fractional calculus [J].

Butzer, PL ;

Kilbas, AA ;

Trujillo, JJ .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2003, 24 (7-8) :673-711

[4] Mechanics with variable-order differential operators [J].

Coimbra, CFM .

ANNALEN DER PHYSIK, 2003, 12 (11-12) :692-703

[5]

Dzherbashyan M. M., 1968, IZV ACAD NAUK ARMJAN, V3, P3

[6] On Caputo modification of the Hadamard fractional derivatives [J].

Gambo, Yusuf Y. ;

Jarad, Fahd ;

Baleanu, Dumitru ;

Abdeljawad, Thabet .

ADVANCES IN DIFFERENCE EQUATIONS, 2014,

[7] Caputo-type modification of the Hadamard fractional derivatives [J].

Jarad, Fahd ;

Abdeljawad, Thabet ;

Baleanu, Dumitru .

ADVANCES IN DIFFERENCE EQUATIONS, 2012,

[8] Finite difference/spectral approximations for the time-fractional diffusion equation [J].

Lin, Yumin ;

Xu, Chuanju .

JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 225 (02) :1533-1552

[9] Noether's theorem for fractional variational problems of variable order [J].

Odzijewicz, Tatiana ;

Malinowska, Agnieszka B. ;

Torres, Delfim F. M. .

CENTRAL EUROPEAN JOURNAL OF PHYSICS, 2013, 11 (06) :691-701

[10] Numerical approximations of fractional derivatives with applications [J].

Pooseh, Shakoor ;

Almeida, Ricardo ;

Torres, Delfim F. M. .

ASIAN JOURNAL OF CONTROL, 2013, 15 (03) :698-712

← 1 2 →