• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.211-222
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• 2020

Integral inequalities provide a very useful and handy tool for the study of qualitative as well as quantitative properties of solutions of differential and integral equations. The main object of this work is to generalize some integral inequalities of quadratic type not only for integer order but also for arbitrary (fractional) order. We also study some inequalities of Pachpatte type.

• 호남수학학술지
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• 제45권1호
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• pp.54-70
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• 2023

In this article, we state and prove several new retarded nonlinear integral and integro-differential inequalities of Gronwall-Bellman-Pachpatte type. These inequalities generalize some former famous inequalities and can be used in examining the existence, uniqueness, boundedness, stability, asymptotic behaviour, quantitative and qualitative properties of solutions of nonlinear differential and integral equations. Applications are provided to demonstrate the strength of our inequalities in estimating the boundedness and global existence of the solution to initial value problem for nonlinear integro-differential equation and Volterra type retarded nonlinear equation. This research work will ensure to open the new opportunities for studying of nonlinear dynamic inequalities on time scale structure of varying nature.

• 충청수학회지
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• 제26권1호
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• pp.71-84
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• 2013

In this paper we study some nonlinear Pachpatte type integral inequalities on time scales by using a Bihari type inequality. Our results unify some continuous inequalities and their corresponding discrete analogues, and extend these inequalities to dynamic inequalities on time scales. Furthermore, we give some examples concerning our results.