"Applied Mathematics" .
"order" .
.
.
"kind" .
"first-order differential equations" .
"differential equations" .
"Advances in Continuous and Discrete Models" .
.
_:Nfda1386c5ad541898a6cf2552935b520 "Springer Nature - SN SciGraph project" .
_:N4bb7b7874ed7402c90fef61ac24c8872 .
"Ayman M." .
.
.
"This article demonstrates the behaviour of solutions to a kind of nonlinear third order neutral stochastic differential equations. Setting x\u2032(t)=y(t)\\documentclass[12pt]{minimal}\n \\usepackage{amsmath}\n \\usepackage{wasysym}\n \\usepackage{amsfonts}\n \\usepackage{amssymb}\n \\usepackage{amsbsy}\n \\usepackage{mathrsfs}\n \\usepackage{upgreek}\n \\setlength{\\oddsidemargin}{-69pt}\n \\begin{document}$x^{\\prime }(t)=y(t)$\\end{document}, y\u2032(t)=z(t)\\documentclass[12pt]{minimal}\n \\usepackage{amsmath}\n \\usepackage{wasysym}\n \\usepackage{amsfonts}\n \\usepackage{amssymb}\n \\usepackage{amsbsy}\n \\usepackage{mathrsfs}\n \\usepackage{upgreek}\n \\setlength{\\oddsidemargin}{-69pt}\n \\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." .
.
.
_:N4bb7b7874ed7402c90fef61ac24c8872 .
"complement" .
.
.
"2022-04-07" .
.
.
_:N488118e503b64ec19e1f5e6476e09b77 .
_:N77e5643960e04dc48c660557293a6bae "dimensions_id" .
.
"solution" .
_:N6d0231213b2e46c39092bfbf5cf6ebc7 "10.1186/s13662-022-03703-x" .
_:N8d4db78347a04ddd84aec231df0dbe3c "2022" .
.
"2022-10-01T06:50" .
"Lyapunov" .
.
"stochastic differential equations" .
"boundedness" .
"system" .
"function" .
.
"stochastic stability" .
.
"Department of Mathematics, Faculty of Science, New Valley University, 72511, El-Khargah, Egypt" .
"https://doi.org/10.1186/s13662-022-03703-x" .
.
.
.
_:Nfda1386c5ad541898a6cf2552935b520 .
_:N77e5643960e04dc48c660557293a6bae .
.
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"2731-4235" .
.
"criteria" .
.
_:N6d0231213b2e46c39092bfbf5cf6ebc7 "doi" .
.
"true"^^ .
"Mathematical Sciences" .
"third-order differential equation" .
.
"effectiveness" .
.
"Mahmoud" .
.
.
"https://scigraph.springernature.com/explorer/license/" .
"hypothesis" .
.
"Department of Mathematics, Faculty of Science, New Valley University, 72511, El-Khargah, Egypt" .
"behavior" .
_:N4bb7b7874ed7402c90fef61ac24c8872 _:Nf384e4bd19a4494589233a32a9fcb38c .
.
_:N77e5643960e04dc48c660557293a6bae .
.
"stability" .
.
"literature" .
.
"Adeleke T." .
_:N6d0231213b2e46c39092bfbf5cf6ebc7 .
.
.
_:Nf384e4bd19a4494589233a32a9fcb38c .
.
"Statistics" .
"neutral stochastic differential equations" .
"article" .
"behavior of solutions" .
"On the behaviour of solutions to a kind of third order neutral stochastic differential equation with delay" .
.
"Springer Nature" .
"Ademola" .
.
"paper complement" .
.
"Department of Mathematics, Obafemi Awolowo University, 220005, Ile-Ife, Nigeria" .
.
.
"28" .
_:N6d0231213b2e46c39092bfbf5cf6ebc7 .
.
_:N77e5643960e04dc48c660557293a6bae "pub.1146947930" .
.
"nonlinear neutral stochastic differential equations" .
"cases" .
.
.
_:N488118e503b64ec19e1f5e6476e09b77 .