Analysis on some powered integral inequalities with retarded argument and application

We investigate a certain class of nonlinear Gronwall-Bellman-Pachpatte type of integral inequalities involving retarded term and nonlinear integrals. Our results derive some new inequalities as well as give an upper bound estimation of the unknown function. The significance of these inequalities ori...

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Bibliographic Details
Published inJournal of Taibah University for Science Vol. 14; no. 1; pp. 488 - 495
Main Author Khan, Zareen A.
Format Journal Article
LanguageEnglish
Published Taylor & Francis 01.01.2020
Taylor & Francis Group
Subjects
explicit bounds
non-decreasing
power
Retarded integral inequalities
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Summary:We investigate a certain class of nonlinear Gronwall-Bellman-Pachpatte type of integral inequalities involving retarded term and nonlinear integrals. Our results derive some new inequalities as well as give an upper bound estimation of the unknown function. The significance of these inequalities originate from the truth that it is far applicable in specific situations in which different available inequalities do not apply legitimately. Our consequences additionally can be used as powerful tools in the analysis of certain classes of differential equations, integral equations, and evolution equations. An example is also illustrated to show the validity of our established theorems.
ISSN:1658-3655
1658-3655
DOI:10.1080/16583655.2020.1747218