scholarly journals On Retarded Integral Inequalities for Dynamic Systems on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qiao-Luan Li ◽  
Xu-Yang Fu ◽  
Zhi-Juan Gao ◽  
Wing-Sum Cheung
Keyword(s):  
Integral Equations ◽  
Time Scales ◽  
Dynamic Systems ◽  
Time Delays ◽  
Integral Inequalities

The object of this paper is to establish some nonlinear retarded inequalities on time scales which can be used as handy tools in the theory of integral equations with time delays.

scholarly journals ON BIVARIATE RETARDED INTEGRAL INEQUALITIES AND THEIR APPLICATIONS

2019 ◽  
pp. 553
Author(s):  
Fuat Usta ◽  
Mehmet Zeki Sarıkaya
Keyword(s):  
Differential Equations ◽  
Integral Equations ◽  
Fractional Order ◽  
Time Delays ◽  
Integral Inequalities ◽  
Partial Differential ◽  
Independent Variables ◽  
Fractional Order Differential Equations ◽  
Two Independent Variables ◽  
Differential And Integral Equations

In this paper, we obtain some retarded integral inequalities in two independent variables which can be used as tools in the theory of partial differential and integral equations with time delays. The presented inequalities are of new forms compared with the existing ones so far in the literature. In order to illustrate the validity of the theorems we give one application for them for the solution to certain fractional order differential equations.

scholarly journals Estimates of Certain Integral Inequalities on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Deepak B. Pachpatte
Keyword(s):  
Integral Equations ◽  
Time Scales ◽  
Integral Inequalities ◽  
Explicit Bounds

The main objective of this paper is to establish explicit bounds on certain integral inequalities on time scales, which can be used as tools in the study of certain classes of integral equations on time scales. Some applications of our results are also given.

scholarly journals Qi Type Diamond-Alpha Integral Inequalities

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 449
Author(s):  
Zhong-Xuan Mao ◽  
Ya-Ru Zhu ◽  
Bao-Hua Guo ◽  
Fu-Hai Wang ◽  
Yu-Hua Yang ◽  
...  
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Integral Inequalities

In this paper, we establish sufficient conditions for Qi type diamond-alpha integral inequalities and its generalized form on time scales.

scholarly journals Nonlinear integral inequalities on time scales with ‘maxima’

2014 ◽  
Vol 2014 (1) ◽  
pp. 255
Author(s):  
Phollakrit Thiramanus ◽  
Jessada Tariboon ◽  
Sotiris K Ntouyas
Keyword(s):  
Time Scales ◽  
Integral Inequalities

scholarly journals Lyapunov stability theory for dynamic systems on time scales

1992 ◽  
Vol 5 (3) ◽  
pp. 275-281 ◽  
Author(s):  
Billur Kaymakçalan
Keyword(s):  
Time Scales ◽  
Lyapunov Stability ◽  
Comparison Principle ◽  
Dynamic Systems ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Existence Theory ◽  
Lyapunov’S Second Method ◽  
Stability Results

By use of the necessary calculus and the fundamental existence theory for dynamic systems on time scales, in this paper, we develop Lyapunov's second method in the framework of general comparison principle so that one can cover and include several stability results for both types of equations at the same time.

scholarly journals Stability analysis in terms of two measures for dynamic systems on time scales

1993 ◽  
Vol 6 (4) ◽  
pp. 325-344 ◽  
Author(s):  
Billûr Kaymakçalan
Keyword(s):  
Stability Analysis ◽  
Time Scales ◽  
Dynamic Systems ◽  
Lyapunov’S Second Method ◽  
Two Measures ◽  
Set Up ◽  
Stability Results ◽  
Stability Concepts ◽  
Single Set

Using the theory of Lyapunov's second method developed earlier for time scales, we extend our stability results to two measures which give rise to unification of several stability concepts in a single set up.

scholarly journals Some Nonlinear Delay Volterra–Fredholm Type Dynamic Integral Inequalities on Time Scales

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Yazhou Tian ◽  
A. A. El-Deeb ◽  
Fanwei Meng
Keyword(s):  
Time Scales ◽  
Qualitative Theory ◽  
Integral Inequalities ◽  
Dynamic Equations ◽  
Fredholm Type ◽  
Explicit Bounds ◽  
Theoretical Results ◽  
Nonlinear Delay

We are devoted to studying a class of nonlinear delay Volterra–Fredholm type dynamic integral inequalities on time scales, which can provide explicit bounds on unknown functions. The obtained results can be utilized to investigate the qualitative theory of nonlinear delay Volterra–Fredholm type dynamic equations. An example is also presented to illustrate the theoretical results.

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