标题：Some new generalized Gronwall-Bellman type discrete fractional inequalities
作者机构：[Feng, QH]Shandong Univ Technol, Sch Sci, Zibo 255049, Shandong, Peoples R China.
通讯作者地址：[Feng, QH]Shandong Univ Technol, Sch Sci, Zibo 255049, Shandong, Peoples R China.
来源：APPLIED MATHEMATICS AND COMPUTATION
关键词：Gronwall-Bellman type inequality; Discrete fractional difference; inequality; Fractional sum inequality; Fractional difference equation;; Boundedness
摘要：In this paper, we present some new generalized Gronwall-Bellman type discrete fractional inequalities including fractional sum inequalities and fractional difference inequalities. These inequalities are of new forms compared with the existing results so far in the literature, and can be used to provide explicit bounds for unknown functions concerned. For illustrating the effectiveness of the presented results, we apply them to research qualitative and quantitative properties for the solutions of an IVP with respect to a fractional difference equation. (C) 2015 Published by Elsevier Inc.