Some Generalizations of ( backward difference backward difference )Δ-Gronwall-Bellman-Pachpatte Dynamic Inequalities on Time Scales with Application

被引：0
|
作者：
El-Deeb, Ahmed A. [1 ]
El-Bary, Alaa A. [2 ,3 ,4 ]
Awrejcewicz, Jan [5 ]
机构：
[1] Al Azhar Univ, Fac Sci, Dept Math, Nasr City 11884, Egypt
[2] Arab Acad Sci Technol & Maritime Transport, Basic & Appl Sci Inst, POB 1029, Alexandria 21532, Egypt
[3] Acad Sci Res & Technol, Natl Comm Math, Cairo 11516, Egypt
[4] Acad Sci Res & Technol, Council Future Studies & Risk Management, Cairo 11516, Egypt
[5] Lodz Univ Technol, Dept Automat Biomech & Mechatron, 1-15 Stefanowski St, PL-90924 Lodz, Poland
来源：
SYMMETRY-BASEL | 2022年 / 14卷 / 09期
关键词：
Gronwall's inequality; dynamic inequality; time scales; Leibniz integral rule on time scales; RETARDED INTEGRAL-INEQUALITIES; 2 INDEPENDENT VARIABLES;
D O I：
10.3390/sym14091823
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
As a new usage of Leibniz integral rule on time scales, we proved some new extensions of dynamic Gronwall-Pachpatte-type inequalities on time scales. Our results extend some existing results in the literature. Some integral and discrete inequalities are obtained as special cases of the main results. The inequalities proved here can be used in the analysis as handy tools to study the stability, boundedness, existence, uniqueness and oscillation behavior for some kinds of partial dynamic equations on time scales. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.
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页数：14
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