Browsing by Author "Yao, J.-C."

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Enhanced Impulsive Stabilization Results of Differential and Integro-Differential Equations of Second Order
(American Institute of Mathematical Sciences, 2026) Tunç, O.; Berezansky, L.; Tunç, C.; Yao, J.-C.
This paper delves into the exponential stabilization of delay differential equations (DDEs) and integro-delay differential equations (IDDEs) of second order including multiple constant retardations. By means of impulsive controls (ICs), we prove that the considered DDEs and IDDEs of second order can be exponentially stabilized. By defining two new Lyapunov-Krasovskiı̆ functionals (LKFs), we prove four new results on the exponential impulsive stabilization of the equations. Two examples are given to show numerical applications of the results. The results of this paper generalize and enhance some recent and related results in the literature. © 2025 Elsevier B.V., All rights reserved.
On the Ulam Stabilities of Nonlinear Integral Equations and Integro-Differential Equations
(John Wiley and Sons Ltd, 2024) Tunç, O.; Tunç, C.; Petruşel, G.; Yao, J.-C.
In this research, two systems of nonlinear Volterra integral equation and Volterra integro-differential equation were considered. New results in sense of Ulam stabilities in relation to these two systems were proved on a finite interval. The proof of the results on the Ulam stabilities of that classes of the equations are based on the nonlinear alternative related to Banach's contraction principle. The outcomes of this research give new contribution to the theory of Ulam stabilities. © 2024 John Wiley & Sons, Ltd.