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Browsing by Author "Wen, Ching-Feng"

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    New Fundamental Results on the Continuous and Discrete Integro-Differential Equations
    (Mdpi, 2022) Tunc, Osman; Tunc, Cemil; Yao, Jen-Chih; Wen, Ching-Feng
    This work studies certain perturbed and un-perturbed nonlinear systems of continuous and discrete integro-delay differential equations (IDDEs). Using the Lyapunov-Krasovskii functional (LKF) method and the Lyapunov-Razumikhin method (LRM), uniform asymptotic stability (UAS), uniform stability (US), integrability and boundedness of solutions as well as exponential stability (ES) and instability of solutions are discussed. In this paper, five new theorems and a corollary are given and three numerical applications are provided with their simulations. With this work, we aim to make new contributions to the theory of the continuous and discrete integro-differential equations.
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    Article
    On the Qualitative Analyses Solutions of New Mathematical Models of Integro-Differential Equations With Infinite Delay
    (Wiley, 2023) Tunc, Cemil; Tunc, Osman; Wen, Ching-Feng; Yao, Jen-Chi
    This paper deals with the uniformly stability (US), globally uniformly asymptotically stability (GUAS) and instability of zero solution as well as integrability and boundedness of nonzero solutions of certain nonlinear integro-differential equations (IDEs). We prove five new theorems, which include sufficient conditions related to these fundamental qualitative properties of solutions to the IDEs considered. The main tools used in the proof are two new and suitable Lyapunov-Krasovskii functionals (LKFs). In particular cases, two numerical examples are given and solved via the fourth order Runge-Kutta method (RKM) in MATLAB to illustrate the theoretical results of this paper. Compared with the existing results on the fundamental qualitative behaviors of scalar IDEs, our results are new, original, more effective and convenient for tests and applications.