Ayman M.
Mahmoud
neutral stochastic differential equations
equations
first-order differential equations
results
28
special case
Lyapunov
nontrivial solutions
delay
reliability
trivial solution
paper complement
boundedness
2022-09-02T16:06
stochastic differential equations
order
system
decisions
differential equations
third-order differential equation
On the behaviour of solutions to a kind of third order neutral stochastic differential equation with delay
solution
function
order differential equations
complement
article
kind
cases
quadratic function
stability
stochastic boundedness
behavior of solutions
literature
behavior
nonlinear neutral stochastic differential equations
2022-04-07
This article demonstrates the behaviour of solutions to a kind of nonlinear third order neutral stochastic differential equations. Setting x′(t)=y(t)\documentclass[12pt]{minimal}
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\begin{document}$x^{\prime }(t)=y(t)$\end{document}, y′(t)=z(t)\documentclass[12pt]{minimal}
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\begin{document}$y^{\prime }(t) =z(t)$\end{document} the third order differential equation is ablated to a system of first order differential equations together with its equivalent quadratic function to derive a suitable downright Lyapunov functional. This functional is utilised to obtain criteria which guarantee stochastic stability of the trivial solution and stochastic boundedness of the nontrivial solutions of the discussed equations. Furthermore, special cases are provided to verify the effectiveness and reliability of our hypotheses. The results of this paper complement the existing decisions on system of nonlinear neutral stochastic differential equations with delay and extend many results on third order neutral and stochastic differential equations with and without delay in the literature.
https://doi.org/10.1186/s13662-022-03703-x
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third order
hypothesis
articles
article
stochastic stability
true
2022-04-07
criteria
Ademola
Adeleke T.
10.1186/s13662-022-03703-x
doi
Department of Mathematics, Obafemi Awolowo University, 220005, Ile-Ife, Nigeria
Department of Mathematics, Obafemi Awolowo University, 220005, Ile-Ife, Nigeria
1687-1839
2731-4235
Advances in Continuous and Discrete Models
Springer Nature
1
Department of Mathematics, Faculty of Science, New Valley University, 72511, El-Khargah, Egypt
Department of Mathematics, Faculty of Science, New Valley University, 72511, El-Khargah, Egypt
Mathematical Sciences
dimensions_id
pub.1146947930
Springer Nature - SN SciGraph project
Statistics
Applied Mathematics
2022