Explicit bounds derived by some new inequalities and applications in fractional integral equations

被引：13
|
作者：
Zheng, Bin [1 ]
机构：
[1] Shandong Univ Technol, Sch Sci, Zibo 255049, Shandong, Peoples R China
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2014年
关键词：
Gronwall-type inequality; explicit bound; fractional differential equation; qualitative analysis; quantitative analysis; NONLINEAR DYNAMIC INEQUALITIES; ITERATION METHOD; TIME SCALES; GRONWALL; BELLMAN; CALCULUS;
D O I：
10.1186/1029-242X-2014-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present some new Gronwall-type inequalities. Explicit bounds for the unknown functions concerned are derived based on these inequalities and the properties of the modified Riemann-Liouville fractional derivative. The inequalities established are of new forms compared with the existing results so far in the literature. For illustrating the validity of the inequalities established, we apply them to research the boundedness, quantitative property, and continuous dependence on the initial value for the solution to a certain fractional integral equation.
引用
收藏
页数：12
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