A Comprehensive View of the Solvability and Stability of a Feedback Control Problem with a State-Dependent Delay Implicit Pantograph Equation

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DOI: https://doi.org/10.28924/2291-8639-22-2024-184
Published: Oct 15, 2024
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Ahmed M.A. El-Sayed, Eman M. Al-Barg, Hanna R. Ebead, A Comprehensive View of the Solvability and Stability of a Feedback Control Problem with a State-Dependent Delay Implicit Pantograph Equation, Int. J. Anal. Appl., 22 (2024), 184.

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Ahmed M.A. El-Sayed, Eman M. Al-Barg, Hanna R. Ebead

Abstract

In this paper, we examine the existence of a unique solution of a feedback control problem with an implicit state-dependent pantograph equation. Additionally, the study implements the problem’s Hyers-Ulam stability and the continuous dependence of the unique solution on the initial data and the parameters. Furthermore, we investigate this problem in the absence of feedback control. We also provide some examples to illustrate our results.

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