Effectiveness of matrix measure in finding periodic solutions for nonlinear systems of differential and integro-differential equations with delays

In this manuscript, under the matrix measure and some sufficient conditions, we will overcame all difficulties and challenges related to the fundamental matrix for a generalized nonlinear neutral functional differential equations in matrix form with multiple delays. The periodicity of solutions, as...

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Published inAIMS mathematics Vol. 9; no. 6; pp. 14274 - 14287
Main Authors Mesmouli, Mouataz Billah, Menaem, Amir Abdel, Hassan, Taher S.
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
arzela-ascoli's theorem
delay
fixed point theorem
matrix measure
periodic solutions
system of differential equations
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Summary:In this manuscript, under the matrix measure and some sufficient conditions, we will overcame all difficulties and challenges related to the fundamental matrix for a generalized nonlinear neutral functional differential equations in matrix form with multiple delays. The periodicity of solutions, as well as the uniqueness under the considered conditions has been proved employing the fixed point theory. Our approach expanded and generalized certain previously published findings for example, we studied the uniqueness of a solution that was absent in some literature. Moreover, an example was given to confirm the main results.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024693