Browsing by Author "Mahmoud, Ayman M."

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Asymptotic Stability of Solutions for a Kind of Third-Order Stochastic Differential Equations With Delays
(Univ Miskolc inst Math, 2019) Mahmoud, Ayman M.; Tunc, Cemil
This work is devoted to investigate the stochastic asymptotically stability of the zero solution for a kind of third-order stochastic differentials equation with variable and constant delays by a suitable Lyapunov functional. Our results improve and form a complement to some results that can be found in the literature. In the last section, we give an example to illustrate our main result.
On the Qualitative Behaviors of Stochastic Delay Integro-Differential Equations of Second Order
(Springer, 2024) Mahmoud, Ayman M.; Tunc, Cemil
In this paper, we investigate the sufficient conditions that guarantee the stability, continuity, and boundedness of solutions for a type of second-order stochastic delay integro-differential equation (SDIDE).To demonstrate the main results, we employ a Lyapunov functional. An example is provided to demonstrate the applicability of the obtained result, which includes the results of this paper and obtains better results than those available in the literature.
Stability and Boundedness of Solutions of a Certain N-Dimensional Nonlinear Delay Differential System of Third-Order
(Walter de Gruyter Gmbh, 2016) Mahmoud, Ayman M.; Tunc, Cemil
In this paper, by defining Lyapunov functionals, we investigate proper sufficient conditions for the uniform stability of the zero solution, and also for the uniform boundedness and uniform ultimate boundedness of all solutions of a certain third-order nonlinear vector delay differential equation of the type (X) triple over dot + A(sic) + A (X) over dot + H(X(t - r)) = P(t).