A general quantum difference calculus

被引：24

作者：

Hamza, Alaa E. ^{[1
]}

Sarhan, Abdel-Shakoor M. ^{[2
]}

Shehata, Enas M. ^{[2
]}

Aldwoah, Khaled A. ^{[3
]}

机构：

[1] Cairo Univ, Fac Sci, Dept Math, Giza, Egypt

[2] Menoufia Univ, Fac Sci, Dept Math, Shibin Al Kawm, Egypt

[3] Islamic Univ Madinah, Fac Sci, Dept Math, Al Madinah Al Munawarah, Saudi Arabia

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2015年

关键词：

quantum difference operator; quantum calculus; Hahn difference operator; Jackson q-difference operator;

D O I：

10.1186/s13662-015-0518-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a strictly increasing continuous function beta, and we present a general quantum difference operator D-beta which is defined to be D(beta)f (t) = (f(beta(t)) -f(t))/(beta(t) - t). This operator yields the Hahn difference operator when beta(t) = qt + omega, the Jackson q-difference operator when beta(t) = qt, q is an element of (0, 1), omega > 0 are fixed real numbers and the forward difference operator when beta(t) = t + omega, omega > 0. A calculus based on the operator D-beta and its inverse is established.

引用

页数：19

共 15 条

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