Honam Mathematical Journal (호남수학학술지)

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RETARDED NONLINEAR INTEGRAL INEQUALITIES OF GRONWALL-BELLMAN-PACHPATTE TYPE AND THEIR APPLICATIONS

  • Abdul Shakoor (Department of Mathematics, The Islamia University of Bahawalpur) ;
  • Mahvish Samar (College of Mathematics and Computer Science, Zhejiang Normal University) ;
  • Samad Wali (Department of Mathematics, Namal University) ;
  • Muzammil Saleem (Department of Mathematics, Aspire Group of Colleges, Sadiq Abad Campus)
  • Received : 2022.03.16
  • Accepted : 2022.11.01
  • Published : 2023.03.25
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Abstract

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.

Keywords

Acknowledgement

The authors would like to thank the editor and the reviewers for their generous time to review and giving valuable comments and suggestions which improve the quality of the paper.

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