New Fundamental Results on the Continuous and Discrete Integro-Differential Equations

Mathematics

Ching-Feng Wen¹  Osman Tunç²  Cemil Tunç³  Jen-Chih Yao⁴ 

[1] Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 80708, Taiwan;Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, Turkey;Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van 65080, Turkey;Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan;

关键词: nonlinear system of IDEs;    stability;    instability;    integrability;    boundedness at infinity;    LKF;   

DOI  :  10.3390/math10091377

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown