Some new variants of interval-valued Gronwall type inequalities on time scales

Some new generalized Gronwall-Bellman-type integral inequalities in two independent variables on time scales

*Correspondence: [email protected] School of Science, Shandong University of Technology, Zhangzhou Road 12, Zibo, Shandong 255049, China Abstract In this paper, some new Gronwall-Bellman-type integral inequalities in two independent variables on time scales are established, which can be used as a handy tool in the research of qualitative and quantitative properties of solutions of dynamic equation...

Some New Gronwall-Bellman-Type Inequalities on Time Scales and Their Applications

In this work, we investigate some new Gronwall-Bellman type dynamic inequalities on time scales in two independent variables, which provide a handy tool in deriving explicit bounds on unknown functions in certain dynamic equations on time scales. The established results generalize the main results on integral inequalities for continuous functions in [1] and their corresponding discrete analysis...

Nonlinear Dynamic Inequalities of Gronwall-Bellman Type on Time Scales

The main aim of this paper is to establish some new explicit bounds of solutions of a certain class of nonlinear dynamic inequalities (with and without delays) of Gronwall-Bellman type on a time scale T which is unbounded above. These on the one hand generalize and on the other hand furnish a handy tool for the study of qualitative as well as quantitative properties of solutions of delay dynami...

Gronwall-OuIang-Type Integral Inequalities on Time Scales

OuIang inequalities and their generalizations have proved to be useful tools in oscillation theory, boundedness theory, stability theory, and other applications of differential and difference equations. A nice introduction to continuous and discrete OuIang inequalities can be found in 1, 2 , and studies in 3–5 give some of their generalizations to multiple integrals and higher-dimensional space...

Some Opial-Type Inequalities on Time Scales

and Applied Analysis 3 where r t is positive and continuous function with ∫X a dt/r t < ∞, and if x b 0, then ∫b X |x t |∣∣x′ t ∣∣dt ≤ 1 2 ∫b

Some Pachpatte type inequalities on time scales