ON THE FRACTIONAL q-DERIVATIVE OF CAPUTO TYPE

被引：0

作者：

Stankovic, Miomir S. l ^{[1
]}

Rajkovic, Predrag M. ^{[2
]}

Marinkovic, Sladjana D. ^{[3
]}

机构：

[1] Univ Nis, Fac Occupat Safety, Nish 18000, Serbia

[2] Univ Nis, Fac Mech Engn, Nish 18000, Serbia

[3] Univ Nis, Fac Elect Engn, Nish 18000, Serbia

来源：

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES | 2010年 / 63卷 / 02期

关键词：

basic hypergeometric functions; fractional calculus; q-integral; q-derivative; fractional integral; fractional derivative; Q-INTEGRALS; CALCULUS;

D O I：

暂无

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Based on the notion of fractional q-integral with the parametric lower limit of integration, we define fractional q-derivatives of Caputo and Riemann-Liouville type. We study some of their properties as well as the relations between them. Also, the compositions of these operators are considered.

引用

页码：197 / 204

页数：8

共 10 条

[1] CERTAIN FRACTIONAL Q-INTEGRALS AND Q-DERIVATIVES [J].

AGARWAL, RP .

PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY-MATHEMATICAL AND PHYSICAL SCIENCES, 1969, 66 :365-&

[2] SOME FRACTIONAL Q-INTEGRALS AND Q-DERIVATIVES [J].

ALSALAM, WA .

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1966, 15 :135-&

[3]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[4] Variational calculus on q-nonuniform lattices [J].

Bangerezako, G .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 306 (01) :161-179

[5] Algorithms for the fractional calculus: A selection of numerical methods [J].

Diethelm, K ;

Ford, NJ ;

Freed, AD ;

Luchko, Y .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2005, 194 (6-8) :743-773

[6]

Gasper G., 2004, ENCY MATH ITS APPL, Vsecond

[7]

Mansour Z. S. I., 2009, FRACT CALC APPL ANAL, V12, P159

[8]

Rajkovic P.M., 2007, Frac. Calc. Appl. Anal, V10, P359

[9] FRACTIONAL INTEGRALS AND DERIVATIVES IN q-CALCULUS [J].

Rajkovic, Predrag M. ;

Marinkovic, Sladana D. ;

Stankovic, Miomir S. .

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2007, 1 (01) :311-323

[10] A generalization of the concept of q-fractional integrals [J].

Rajkovic, Predrag M. ;

Marinkovic, Sladjana D. ;

Stankovic, Miomir S. .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2009, 25 (10) :1635-1646

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