On the properties of solutions for nonautonomous third-order stochastic differential equation with a constant delay

Authors

AYMAN MOHAMMED MAHMOUD
DOAA ALI MOHAMED BAKHIT

DOI

10.55730/1300-0098.3351

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.

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