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<p>In this paper, using the comparison theorem on time scales and some elementary algebraic inequalities, we introduce a new class of generalizations of Pachpatte-type inequalities and their extensions on time scales, which provide explicit bounds on unknown functions. Some applications of the main results for specific nonlinear dynamic equations are given at the end of this paper.</p>

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On Some Pachpatte-Type Dynamic Inequalities and Their Applications

  • 期刊论文

  • 发表日期：

    2025年5月13日

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  • Mahmoud M. Osman,
  • Samir H. Saker,
  • Douglas R. Anderson

摘要

In this paper, using the comparison theorem on time scales and some elementary algebraic inequalities, we introduce a new class of generalizations of Pachpatte-type inequalities and their extensions on time scales, which provide explicit bounds on unknown functions. Some applications of the main results for specific nonlinear dynamic equations are given at the end of this paper.