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.
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页码：1602 / 1611
页数：10
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