A variety of dynamic inequalities on time scales with retardation

Volume 11, Issue 10, pp 1185--1206 http://dx.doi.org/10.22436/jnsa.011.10.07

Publication Date: July 22, 2018 Submission Date: December 07, 2017 Revision Date: December 21, 2017 Accteptance Date: March 25, 2018

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Authors

A. A. El-Deeb - Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt. Wing-Sum Cheung - Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong.

Abstract

In this paper, we will prove some new nonlinear retarded dynamic inequalities of Gronwall-Bellman type on time scales. These inequalities are of new forms compared with the existing results so far in the literature, which can be used as effective tools in the study of certain nonlinear retarded dynamic equations. Some special cases of our results contain continuous Gronwall-type inequalities and their discrete analogues. We also indicate some application examples to illustrate our results at the end.

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Keywords

• Gronwall's inequality
• Young's inequality
• time scales

MSC

•  26A15
•  39A12
•  34A12
•  34A40
•  26D10
•  26D15
•  26D20

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