On Riemann and Caputo fractional differences

被引：546

作者：

Abdeljawad, Thabet ^{[1
]}

机构：

[1] Cankaya Univ, Dept Math & Comp Sci, TR-06530 Ankara, Turkey

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 62卷 / 03期

关键词：

Left fractional sum; Right fractional sum; Caputo left and right fractional differences; Left and right Riemann differences; Discrete Mittag-Leffler function; EQUATIONS; DERIVATIVES; CALCULUS;

D O I：

10.1016/j.camwa.2011.03.036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we define left and right Caputo fractional sums and differences, study some of their properties and then relate them to Riemann-Liouville ones studied before by Miller K. S. and Ross B., Atici F.M. and Eloe P. W., Abdeljawad T. and Baleanu D., and a few others. Also, the discrete version of the Q-operator is used to relate the left and right Caputo fractional differences. A Caputo fractional difference equation is solved. The solution proposes discrete versions of Mittag-Leffler functions. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1602 / 1611

页数：10

共 22 条

[1] On the existence and the uniqueness theorem for fractional differential equations with bounded delay within Caputo derivatives [J].

Abdeljawad, Thabet ;

Jarad, Fahd ;

Baleanu, Dumitru .

SCIENCE IN CHINA SERIES A-MATHEMATICS, 2008, 51 (10) :1775-1786

[2] Existence and uniqueness theorem for a class of delay differential equations with left and right Caputo fractional derivatives [J].

Abdeljawad, Thabet ;

Baleanu, Dumitru ;

Jarad, Fahd .

JOURNAL OF MATHEMATICAL PHYSICS, 2008, 49 (08)

[3]

Abdeljawad T, 2011, J COMPUT ANAL APPL, V13, P574

[4] A Hamiltonian formulation and a direct numerical scheme for Fractional Optimal Control Problems [J].

Agrawal, Om P. ;

Baleanu, Dumitru .

JOURNAL OF VIBRATION AND CONTROL, 2007, 13 (9-10) :1269-1281

[5]

[Anonymous], 1989, ELLIS HORWOOD SERIES

[6]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[7]

[Anonymous], ELECT J QUALITATIVE

[8]

[Anonymous], 2006, Journal of the Electrochemical Society

[9]

[Anonymous], 1993, THEORY APPL

[10] On a class of differential equations with left and right fractional derivatives [J].

Atanackovic, T. M. ;

Stankovic, B. .

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2007, 87 (07) :537-546

← 1 2 3 →