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Discontinuity, Nonlinearity, and Complexity 14(2) (2025) 259--267 | DOI:10.5890/DNC.2025.06.001

Harisha Chintamaneni$^{1,2}$, Venkata Appa Rao Bhogapurapu$^{1}$, Sreenivasulu Ayyalappagari$^{1}$

$^{1}$ Department of Engineering Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur, 522302, Andhra Pradesh, India

$^{2}$ Department of Mathematics, Malla Reddy Institute of Technology and Science, Dhulappaly, Secunderabad, Telangana 500100, India

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Abstract

The primary aim of this paper is to identify periodic solutions within an almost linear Volterra Integro-dynamic matrix Sylvester system operating on measure chains. Initially, we undertake a transformation of the Volterra Integro-dynamic matrix Sylvester system into the Kronecker Product Volterra Integro-dynamic System on measure chains through vectorization operations. Subsequent to this transformation, we proceed to establish the existence of periodic solutions for the Kronecker Product Volterra Integro-dynamic system on measure chains, by using Banach fixed point theorem. Importantly, our investigation extends to encompass periodic measure chains operating under both continuous and discrete conditions.

Acknowledgments

The authors would like to express their sincere thanks to the editor and anonymous reviewers for constructive comments and suggestions to improve the quality of this paper.

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