Abstract
In this paper, we develop a fundamental dynamic inequality, a generalization of comparison theorem and reproduce the proofs of some nonlinear integral Pachpatte’s inequalities by using their continuous analogue. We also unify and extend these improved integral Pachpatte’s inequalities and their corresponding discrete analogues on arbitrary time scales. The results are used to make qualitative analysis of higher order dynamic equations.
Highlights
Modeling of some real world problem requires using a dynamic system which involves both discrete and continuous times
6 Conclusion It has been shown that by using mean value theorem, a fundamental dynamic inequality is justifiable on any arbitrary time scale
The cases for some special time scales are as follows: For T = Z, the inequality coincides with the fundamental finite difference inequality presented by Pachpatte in ([17], Theorem 2.3.4)
Summary
Modeling of some real world problem requires using a dynamic system which involves both discrete and continuous times. The authors of [14] established some new inequalities of Pachpatte type, incorporating two nonlinear integral terms, which are themselves the generalizations and refinements of many existing results. The authors in [18] used some dynamic inequalities to show basic qualitative properties of solutions of a certain nonlinear integrodifferential equation on time scales.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call