On the Fundamental Analyses of Solutions to Nonlinear Integro-Differential Equations of the Second Order

Cemil Tunç () and Osman Tunç
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Cemil Tunç: Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van 65080, Turkey
Osman Tunç: Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, Turkey

Mathematics, 2022, vol. 10, issue 22, 1-18

Abstract: In this article, a scalar nonlinear integro-differential equation of second order and a non-linear system of integro-differential equations with infinite delays are considered. Qualitative properties of solutions called the global asymptotic stability, integrability and boundedness of solutions of the second-order scalar nonlinear integro-differential equation and the nonlinear system of nonlinear integro-differential equations with infinite delays are discussed. In the article, new explicit qualitative conditions are presented for solutions of both the second-order scalar nonlinear integro-differential equations with infinite delay and the nonlinear system of integro-differential equations with infinite delay. The proofs of the main results of the article are based on two new Lyapunov–Krasovskiĭ functionals. In particular cases, the results of the article are illustrated with three numerical examples, and connections to known tests are discussed. The main novelty and originality of this article are that the considered integro-differential equation and system of integro-differential equations with infinite delays are new mathematical models, the main six qualitative results given are also new.

Keywords: integro-differential equation; integro-differential system; first order; second order; infinite delay; global asymptotic stability; boundedness; integrability; LKF (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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