scholarly journals Boundedness of the Solutions to Certain Delay Dynamic Integrodifferential Systems on Time Scales

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Min Fan ◽  
Yazhou Tian
Keyword(s):  
Time Scales ◽  
Integral Inequality ◽  
Boundedness Of Solutions ◽  
Delay Integral Inequality

In this paper, the bounds on the solutions of certain delay dynamic integrodifferential systems on time scales are considered. Based on a new Gronwall-Bellman type delay integral inequality, we can estimate the boundedness of solutions to integrodifferential systems. At the end, an example is presented to state the main results.

scholarly journals Properties of Some Partial Dynamic Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Deepak B. Pachpatte
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Point Theorem ◽  
Integral Inequality ◽  
Dynamic Equation ◽  
Dynamic Equations ◽  
Banach Fixed Point Theorem

The main objective of the paper is to study the properties of the solution of a certain partial dynamic equation on time scales. The tools employed are based on the application of the Banach fixed-point theorem and a certain integral inequality with explicit estimates on time scales.

scholarly journals Some Differential Inequalities on Time Scales and Their Applications to Feedback Control Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Yonghong Fan ◽  
Yangyang Yu ◽  
Linlin Wang
Keyword(s):  
Feedback Control ◽  
Control Systems ◽  
Time Scales ◽  
New Method ◽  
Differential Inequalities ◽  
Boundedness Of Solutions ◽  
Ultimate Boundedness ◽  
Uniform Ultimate Boundedness ◽  
Feedback Control Systems

This paper deals with feedback control systems on time scales. Firstly, we generalize the semicycle concept to time scales and then establish some differential inequalities on time scales. Secondly, as applications of these inequalities, we study the uniform ultimate boundedness of solutions of these systems. We give a new method to investigate the permanence of ecosystem on time scales. And some known results have been generalized. Finally, an example is given to support the result.

scholarly journals Some New Delay Integral Inequalities in Two Independent Variables on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
Bin Zheng ◽  
Yaoming Zhang ◽  
Qinghua Feng
Keyword(s):  
Time Scales ◽  
Integral Inequalities ◽  
Dynamic Equations ◽  
Boundedness Of Solutions ◽  
Independent Variables ◽  
Discrete Analysis ◽  
Delay Dynamic Equations ◽  
Two Independent Variables

Some new Gronwall-Bellman-type delay integral inequalities in two independent variables on time scales are established, which can be used as a handy tool in the research of boundedness of solutions of delay dynamic equations on time scales. Some of the established results are 2D extensions of several known results in the literature, while some results unify existing continuous and discrete analysis.

scholarly journals Steffensen's Integral Inequality on Time Scales

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
Umut Mutlu Ozkan ◽  
Hüseyin Yildirim
Keyword(s):  
Time Scales ◽  
Integral Inequality

scholarly journals Integral Inequality of Hardy-Type on Time Scales

2019 ◽  
Vol 09 (06) ◽  
pp. 534-543
Author(s):  
Emmanuella Ehui Aribike ◽  
Yisa Oluwatoyin Anthonio ◽  
Kamilu Rauf ◽  
Michael Oyelami Ajisope
Keyword(s):  
Time Scales ◽  
Integral Inequality ◽  
Hardy Type

scholarly journals Oscillation criteria for a class of third-order Emden–Fowler delay dynamic equations with sublinear neutral terms on time scales

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhiyu Zhang ◽  
Ruihua Feng
Keyword(s):  
Time Scales ◽  
Integral Inequality ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Oscillation Criteria ◽  
Delay Dynamic Equations

AbstractIn this paper, we study the oscillation of a class of third-order Emden–Fowler delay dynamic equations with sublinear neutral terms on time scales. By using Riccati transformation and integral inequality, we establish several new theorems to ensure that each solution of the equation oscillates or asymptotically approaches zero, and the results in the literature are supplemented and extended. Examples are given to illustrate our main results.

Sign in / Sign up

Export Citation Format

Share Document