On the behaviour of solutions to a kind of third order neutral stochastic differential equation with delay View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2022-04-07

AUTHORS

Ayman M. Mahmoud, Adeleke T. Ademola

ABSTRACT

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} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$x^{\prime }(t)=y(t)$\end{document}, y′(t)=z(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \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. More... »

PAGES

28

Identifiers

URI

http://scigraph.springernature.com/pub.10.1186/s13662-022-03703-x

DOI

http://dx.doi.org/10.1186/s13662-022-03703-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1146947930


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0102", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Applied Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0104", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Statistics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Mathematics, Faculty of Science, New Valley University, 72511, El-Khargah, Egypt", 
          "id": "http://www.grid.ac/institutes/grid.252487.e", 
          "name": [
            "Department of Mathematics, Faculty of Science, New Valley University, 72511, El-Khargah, Egypt"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Mahmoud", 
        "givenName": "Ayman M.", 
        "id": "sg:person.012115040631.22", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012115040631.22"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematics, Obafemi Awolowo University, 220005, Ile-Ife, Nigeria", 
          "id": "http://www.grid.ac/institutes/grid.10824.3f", 
          "name": [
            "Department of Mathematics, Obafemi Awolowo University, 220005, Ile-Ife, Nigeria"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Ademola", 
        "givenName": "Adeleke T.", 
        "id": "sg:person.010261047076.03", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010261047076.03"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1186/s13662-017-1102-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1083863740", 
          "https://doi.org/10.1186/s13662-017-1102-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4684-9467-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1007143588", 
          "https://doi.org/10.1007/978-1-4684-9467-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11432-018-9755-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1120394775", 
          "https://doi.org/10.1007/s11432-018-9755-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-94-017-1965-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033261446", 
          "https://doi.org/10.1007/978-94-017-1965-0"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1186/s13662-020-2520-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1124664423", 
          "https://doi.org/10.1186/s13662-020-2520-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4615-9968-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006431894", 
          "https://doi.org/10.1007/978-1-4615-9968-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-4342-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050475850", 
          "https://doi.org/10.1007/978-1-4612-4342-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-9892-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021421011", 
          "https://doi.org/10.1007/978-1-4612-9892-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1186/s13662-018-1721-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1106330703", 
          "https://doi.org/10.1186/s13662-018-1721-9"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2022-04-07", 
    "datePublishedReg": "2022-04-07", 
    "description": "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\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$x^{\\prime }(t)=y(t)$\\end{document}, y\u2032(t)=z(t)\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\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.", 
    "genre": "article", 
    "id": "sg:pub.10.1186/s13662-022-03703-x", 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1052613", 
        "issn": [
          "1687-1839", 
          "2731-4235"
        ], 
        "name": "Advances in Continuous and Discrete Models", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "2022"
      }
    ], 
    "keywords": [
      "neutral stochastic differential equations", 
      "stochastic differential equations", 
      "order differential equations", 
      "differential equations", 
      "behavior of solutions", 
      "nonlinear neutral stochastic differential equations", 
      "third-order differential equation", 
      "first-order differential equations", 
      "stochastic stability", 
      "stochastic boundedness", 
      "trivial solution", 
      "nontrivial solutions", 
      "equations", 
      "special case", 
      "third order", 
      "quadratic function", 
      "paper complement", 
      "solution", 
      "Lyapunov", 
      "boundedness", 
      "delay", 
      "system", 
      "kind", 
      "behavior", 
      "function", 
      "results", 
      "stability", 
      "order", 
      "effectiveness", 
      "reliability", 
      "cases", 
      "criteria", 
      "literature", 
      "article", 
      "complement", 
      "decisions", 
      "hypothesis"
    ], 
    "name": "On the behaviour of solutions to a kind of third order neutral stochastic differential equation with delay", 
    "pagination": "28", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1146947930"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1186/s13662-022-03703-x"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1186/s13662-022-03703-x", 
      "https://app.dimensions.ai/details/publication/pub.1146947930"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-10-01T06:50", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20221001/entities/gbq_results/article/article_938.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1186/s13662-022-03703-x"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1186/s13662-022-03703-x'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1186/s13662-022-03703-x'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1186/s13662-022-03703-x'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1186/s13662-022-03703-x'


 

This table displays all metadata directly associated to this object as RDF triples.

144 TRIPLES      21 PREDICATES      70 URIs      52 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1186/s13662-022-03703-x schema:about anzsrc-for:01
2 anzsrc-for:0102
3 anzsrc-for:0104
4 schema:author N9ce84f264ad345b38a3792f4eb1a266f
5 schema:citation sg:pub.10.1007/978-1-4612-4342-7
6 sg:pub.10.1007/978-1-4612-9892-2
7 sg:pub.10.1007/978-1-4615-9968-5
8 sg:pub.10.1007/978-1-4684-9467-9
9 sg:pub.10.1007/978-94-017-1965-0
10 sg:pub.10.1007/s11432-018-9755-7
11 sg:pub.10.1186/s13662-017-1102-9
12 sg:pub.10.1186/s13662-018-1721-9
13 sg:pub.10.1186/s13662-020-2520-7
14 schema:datePublished 2022-04-07
15 schema:datePublishedReg 2022-04-07
16 schema:description 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} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$x^{\prime }(t)=y(t)$\end{document}, y′(t)=z(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \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.
17 schema:genre article
18 schema:isAccessibleForFree true
19 schema:isPartOf N279fb7de216f4d6797acc3fdd9f451d3
20 Nfa60251d42344f7e9713b07fec63c66b
21 sg:journal.1052613
22 schema:keywords Lyapunov
23 article
24 behavior
25 behavior of solutions
26 boundedness
27 cases
28 complement
29 criteria
30 decisions
31 delay
32 differential equations
33 effectiveness
34 equations
35 first-order differential equations
36 function
37 hypothesis
38 kind
39 literature
40 neutral stochastic differential equations
41 nonlinear neutral stochastic differential equations
42 nontrivial solutions
43 order
44 order differential equations
45 paper complement
46 quadratic function
47 reliability
48 results
49 solution
50 special case
51 stability
52 stochastic boundedness
53 stochastic differential equations
54 stochastic stability
55 system
56 third order
57 third-order differential equation
58 trivial solution
59 schema:name On the behaviour of solutions to a kind of third order neutral stochastic differential equation with delay
60 schema:pagination 28
61 schema:productId N7d5b204be2dc4e6bb3524fdfac58e946
62 N8623c1ac5912477cb3d4cb84971a8d03
63 schema:sameAs https://app.dimensions.ai/details/publication/pub.1146947930
64 https://doi.org/10.1186/s13662-022-03703-x
65 schema:sdDatePublished 2022-10-01T06:50
66 schema:sdLicense https://scigraph.springernature.com/explorer/license/
67 schema:sdPublisher Na89ed9879355423f83ddd73fd7757194
68 schema:url https://doi.org/10.1186/s13662-022-03703-x
69 sgo:license sg:explorer/license/
70 sgo:sdDataset articles
71 rdf:type schema:ScholarlyArticle
72 N279fb7de216f4d6797acc3fdd9f451d3 schema:volumeNumber 2022
73 rdf:type schema:PublicationVolume
74 N3b7b15be992f45a2827fcbb729ffc87b rdf:first sg:person.010261047076.03
75 rdf:rest rdf:nil
76 N7d5b204be2dc4e6bb3524fdfac58e946 schema:name dimensions_id
77 schema:value pub.1146947930
78 rdf:type schema:PropertyValue
79 N8623c1ac5912477cb3d4cb84971a8d03 schema:name doi
80 schema:value 10.1186/s13662-022-03703-x
81 rdf:type schema:PropertyValue
82 N9ce84f264ad345b38a3792f4eb1a266f rdf:first sg:person.012115040631.22
83 rdf:rest N3b7b15be992f45a2827fcbb729ffc87b
84 Na89ed9879355423f83ddd73fd7757194 schema:name Springer Nature - SN SciGraph project
85 rdf:type schema:Organization
86 Nfa60251d42344f7e9713b07fec63c66b schema:issueNumber 1
87 rdf:type schema:PublicationIssue
88 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
89 schema:name Mathematical Sciences
90 rdf:type schema:DefinedTerm
91 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
92 schema:name Applied Mathematics
93 rdf:type schema:DefinedTerm
94 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
95 schema:name Statistics
96 rdf:type schema:DefinedTerm
97 sg:journal.1052613 schema:issn 1687-1839
98 2731-4235
99 schema:name Advances in Continuous and Discrete Models
100 schema:publisher Springer Nature
101 rdf:type schema:Periodical
102 sg:person.010261047076.03 schema:affiliation grid-institutes:grid.10824.3f
103 schema:familyName Ademola
104 schema:givenName Adeleke T.
105 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010261047076.03
106 rdf:type schema:Person
107 sg:person.012115040631.22 schema:affiliation grid-institutes:grid.252487.e
108 schema:familyName Mahmoud
109 schema:givenName Ayman M.
110 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012115040631.22
111 rdf:type schema:Person
112 sg:pub.10.1007/978-1-4612-4342-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050475850
113 https://doi.org/10.1007/978-1-4612-4342-7
114 rdf:type schema:CreativeWork
115 sg:pub.10.1007/978-1-4612-9892-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021421011
116 https://doi.org/10.1007/978-1-4612-9892-2
117 rdf:type schema:CreativeWork
118 sg:pub.10.1007/978-1-4615-9968-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006431894
119 https://doi.org/10.1007/978-1-4615-9968-5
120 rdf:type schema:CreativeWork
121 sg:pub.10.1007/978-1-4684-9467-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007143588
122 https://doi.org/10.1007/978-1-4684-9467-9
123 rdf:type schema:CreativeWork
124 sg:pub.10.1007/978-94-017-1965-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033261446
125 https://doi.org/10.1007/978-94-017-1965-0
126 rdf:type schema:CreativeWork
127 sg:pub.10.1007/s11432-018-9755-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1120394775
128 https://doi.org/10.1007/s11432-018-9755-7
129 rdf:type schema:CreativeWork
130 sg:pub.10.1186/s13662-017-1102-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1083863740
131 https://doi.org/10.1186/s13662-017-1102-9
132 rdf:type schema:CreativeWork
133 sg:pub.10.1186/s13662-018-1721-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1106330703
134 https://doi.org/10.1186/s13662-018-1721-9
135 rdf:type schema:CreativeWork
136 sg:pub.10.1186/s13662-020-2520-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1124664423
137 https://doi.org/10.1186/s13662-020-2520-7
138 rdf:type schema:CreativeWork
139 grid-institutes:grid.10824.3f schema:alternateName Department of Mathematics, Obafemi Awolowo University, 220005, Ile-Ife, Nigeria
140 schema:name Department of Mathematics, Obafemi Awolowo University, 220005, Ile-Ife, Nigeria
141 rdf:type schema:Organization
142 grid-institutes:grid.252487.e schema:alternateName Department of Mathematics, Faculty of Science, New Valley University, 72511, El-Khargah, Egypt
143 schema:name Department of Mathematics, Faculty of Science, New Valley University, 72511, El-Khargah, Egypt
144 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...