Turkish Journal of Mathematics
Abstract
In this work, complete Lyapunov functionals (LFs) are constructed and used for the established conditions on the nonlinear functions appearing in the main equation, to guarantee stochastically asymptotically stable (SAS), uniformly stochastically bounded (USB) and uniformly exponentially asymptotically stable (UEAS) in probability of solutions to the nonautonomous third-order stochastic differential equation (SDE) with a constant delay as \begin{align*} \begin{split} \dddot{x}(t)&+a(t)f(x(t),\dot{x}(t))\ddot{x}(t)+b(t)\phi(x(t))\dot{x}(t) +c(t)\psi(x(t-r))\\&+g(t,x)\dot{\omega}(t)=p(t,x(t),\dot{x}(t),\ddot{x}(t)). \end{split} \end{align*} In Section 4, we give two numerical examples as an application to illustrate the results.
DOI
10.55730/1300-0098.3351
Keywords
(DDE), (SDE), (SDDE), (SAS), (USB), (UEAS)
First Page
135
Last Page
158
Recommended Citation
MAHMOUD, AYMAN MOHAMMED and BAKHIT, DOAA ALI MOHAMED
(2023)
"On the properties of solutions for nonautonomous third-order stochastic differential equation with a constant delay,"
Turkish Journal of Mathematics: Vol. 47:
No.
1, Article 10.
https://doi.org/10.55730/1300-0098.3351
Available at:
https://journals.tubitak.gov.tr/math/vol47/iss1/10
