Reconstruction of nonlinear integral inequalities associated with time scales calculus

In this paper, we build up some generalizations of nonlinear integral inequalities and recreate the results of some Pachpatte’s inequalities on time scales. We not just settle new estimated bounds of a particular class of nonlinear retarded dynamic inequalities, but additionally determine and unify...

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Bibliographic Details
Published inAdvances in difference equations Vol. 2020; no. 1; pp. 1 - 18
Main Author Khan, Zareen A.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 23.07.2020
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Calculus
Difference and Functional Equations
Dynamic equations
Functional Analysis
Inequalities
Integral Pachpatte’s inequalities
Integrals
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Time
Time scales
26E70
Dynamic equations
Integral Pachpatte’s inequalities
Time scales
34N05
35A23
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Summary:In this paper, we build up some generalizations of nonlinear integral inequalities and recreate the results of some Pachpatte’s inequalities on time scales. We not just settle new estimated bounds of a particular class of nonlinear retarded dynamic inequalities, but additionally determine and unify continuous analogs alongside a subjective time scale T . We demonstrate applications of the treated inequalities to reflect the benefits of our work. The key effects will be proven by using the analysis procedure and the standard time-scale comparison theorem technique.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-02842-3