Certain Novel Dynamic Inequalities Applicable in the Theory of Retarded Dynamic Equations and Their Applications

Sujata Bhamre, Nagesh Kale, Subhash Kendre () and James Peters
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Sujata Bhamre: Department of Applied Science and Humanities, Pimpri Chinchwad College of Engineering, Pune 411044, India
Nagesh Kale: Department of Mathematics, Sant Rawool Maharaj Mahavidyalaya, Kudal, Sindhudurg 416520, India
Subhash Kendre: Department of Mathematics, Savitribai Phule Pune University, Pune 411007, India
James Peters: Department of Electrical & Computer Engineering, Computationally Intelligent Systems & Signals Laboratory, University of Manitoba, WPG, Winnipeg, MB R3T 5V6, Canada

Mathematics, 2024, vol. 12, issue 3, 1-18

Abstract: In this article, we establish certain time-scale-retarded dynamic inequalities that contain nonlinear retarded integral equations on various time scales. These inequalities extend and generalize some significant inequalities existing in the literature to their more general forms. The qualitative and quantitative characteristics of solutions to various dynamic equations on time scales involving retarded integrals can be studied using these inequalities. The results presented in this manuscript furnish a powerful tool to analyze the boundedness of nonlinear integral equations with retarded integrals on several time scales. In the end, we also include numerical illustrations to signify the applicability of these results to power nonlinear retarded integral equations on real and quantum time scales.

Keywords: retarded dynamic inequality; dynamic equations; Pachpatte inequalities; time scales (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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