Some New Dynamic Gronwall-Bellman Type Inequalities With Delay on Time Scales and Certain Applications
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Abstract
The main objective of the present article is to prove some new delay nonlinear dynamic inequalities of Gronwall-Bellman-Pachpatte type on time scales. We introduce very important generalized results with the help of Leibniz integral rule on time scales. For some specific time scales, we further show some relevant inequalities as special cases: integral inequalities and discrete inequalities. Our results can be used as handy tools for the study of qualitative and quantitative properties of solutions of dynamic equations on time scales. Some examples are provided to demonstrate the applications of the results.
Description
Eldeeb, Ahmed/0000-0003-2822-4092
ORCID
Keywords
Dynamic Gronwall Type Inequality, Time Scales, Leibniz Integral Rule On Time Scales, Dynamic Gronwall type inequality, Leibniz integral rule on time scales, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Quantum mechanics, QA1-939, FOS: Mathematics, Time Scales, Biology, Anomalous Diffusion Modeling and Analysis, Ecology, Applied Mathematics, Physics, Time scales, Applied mathematics, Nonlocal Partial Differential Equations and Boundary Value Problems, Inequality, Modeling and Simulation, FOS: Biological sciences, Physical Sciences, Nonlinear system, Dynamic equation, Type (biology), Mathematics, dynamic Gronwall-type inequality, Real analysis on time scales or measure chains, time scales, Inequalities involving derivatives and differential and integral operators, Inequalities for sums, series and integrals
Fields of Science
01 natural sciences, 0101 mathematics
Citation
El-Deeb, Ahmed A.; Baleanu, Dumitru (2022). "Some new dynamic Gronwall-Bellman-Pachpatte type inequalities with delay on time scales and certain applications", Journal of Inequalities and Applications, Vol. 2022, No. 1.
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10
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2022
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1
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