文章基本信息

标题：Theory of n th-order linear general quantum difference equations
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作者：Nashat Faried ; Enas M. Shehata ; Rasha M. El Zafarani 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2018
卷号：2018
期号：1
页码：264
DOI：10.1186/s13662-018-1715-7
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we derive the solutions of homogeneous and non-homogeneous nth-order linear general quantum difference equations based on the general quantum difference operator D β $D_{\beta }$ which is defined by D β f ( t ) = ( f ( β ( t ) ) − f ( t ) ) / ( β ( t ) − t ) $D_{\beta }{f(t)}= (f(\beta (t))-f(t) )/ (\beta (t)-t )$ , β ( t ) ≠ t $\beta (t)\neq t$ , where β is a strictly increasing continuous function defined on an interval I ⊆ R $I\subseteq \mathbb{R}$ that has only one fixed point s 0 ∈ I $s_(\in {I}$ . We also give the sufficient conditions for the existence and uniqueness of solutions of the β-Cauchy problem of these equations. Furthermore, we present the fundamental set of solutions when the coefficients are constants, the β-Wronskian associated with D β $D_{\beta }$ , and Liouville’s formula for the β-difference equations. Finally, we introduce the undetermined coefficients, the variation of parameters, and the annihilator methods for the non-homogeneous β-difference equations.