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THEORETICAL AND NUMERICAL ANALYSIS OF PIECEWISE LOTKA–VOLTERRA PREY–PREDATOR MODELS WITH STOCHASTIC DIFFERENTIAL OPERATORS.

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Title: THEORETICAL AND NUMERICAL ANALYSIS OF PIECEWISE LOTKA–VOLTERRA PREY–PREDATOR MODELS WITH STOCHASTIC DIFFERENTIAL OPERATORS.
Authors: KUMAR, ATUL1 (AUTHOR) atul1230123@gmail.com, EMADIFAR, HOMAN1,2 (AUTHOR) homan_emadi@yahoo.com, ALQUDAH, MANAR3 (AUTHOR) maalqudah@pnu.edu.sa, SHAH, KAMAL4 (AUTHOR) kshah@psu.edu.sa, ABDELJAWAD, THABET4,5,6,7 (AUTHOR) tabdeljawad@psu.edu.sa
Source: Fractals. 2026, Vol. 34 Issue 6, p1-15. 15p.
Subjects: Lotka-Volterra equations, Caputo fractional derivatives, Predation, Fractional calculus, Iterative methods (Mathematics), Stochastic analysis, Numerical analysis
Abstract: This paper proposes a collection of nonlinear differential operators. The goal of the work is to develop certain theoretical and analytical intuitions regarding the replacement of the general deferential operators with the derivatives of Caputo, Atangana–Baleanu, and Caputo–Fabrizio. A variety of well-known methodologies were used to examine the models. The Lagrange interpolation polynomial was used to establish a numerical method to solve the models under investigations. We have investigated the related perspective on existence and uniqueness through this work. Several numerical findings were incorporated. The updated models examine the impact of competition on prey and predator abundance. A species' variations in abundance are modeled as a function of the abundance of its competitors; the specific competitive mechanism is neither investigated nor stated in explicit terms. [ABSTRACT FROM AUTHOR]
Copyright of Fractals is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 194008138
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Label: Title
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  Data: THEORETICAL AND NUMERICAL ANALYSIS OF PIECEWISE LOTKA–VOLTERRA PREY–PREDATOR MODELS WITH STOCHASTIC DIFFERENTIAL OPERATORS.
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  Data: <searchLink fieldCode="AR" term="%22KUMAR%2C+ATUL%22">KUMAR, ATUL</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> atul1230123@gmail.com</i><br /><searchLink fieldCode="AR" term="%22EMADIFAR%2C+HOMAN%22">EMADIFAR, HOMAN</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> homan_emadi@yahoo.com</i><br /><searchLink fieldCode="AR" term="%22ALQUDAH%2C+MANAR%22">ALQUDAH, MANAR</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> maalqudah@pnu.edu.sa</i><br /><searchLink fieldCode="AR" term="%22SHAH%2C+KAMAL%22">SHAH, KAMAL</searchLink><relatesTo>4</relatesTo> (AUTHOR)<i> kshah@psu.edu.sa</i><br /><searchLink fieldCode="AR" term="%22ABDELJAWAD%2C+THABET%22">ABDELJAWAD, THABET</searchLink><relatesTo>4,5,6,7</relatesTo> (AUTHOR)<i> tabdeljawad@psu.edu.sa</i>
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  Data: <searchLink fieldCode="JN" term="%22Fractals%22">Fractals</searchLink>. 2026, Vol. 34 Issue 6, p1-15. 15p.
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Lotka-Volterra+equations%22">Lotka-Volterra equations</searchLink><br /><searchLink fieldCode="DE" term="%22Caputo+fractional+derivatives%22">Caputo fractional derivatives</searchLink><br /><searchLink fieldCode="DE" term="%22Predation%22">Predation</searchLink><br /><searchLink fieldCode="DE" term="%22Fractional+calculus%22">Fractional calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+analysis%22">Stochastic analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper proposes a collection of nonlinear differential operators. The goal of the work is to develop certain theoretical and analytical intuitions regarding the replacement of the general deferential operators with the derivatives of Caputo, Atangana–Baleanu, and Caputo–Fabrizio. A variety of well-known methodologies were used to examine the models. The Lagrange interpolation polynomial was used to establish a numerical method to solve the models under investigations. We have investigated the related perspective on existence and uniqueness through this work. Several numerical findings were incorporated. The updated models examine the impact of competition on prey and predator abundance. A species' variations in abundance are modeled as a function of the abundance of its competitors; the specific competitive mechanism is neither investigated nor stated in explicit terms. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Fractals is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1142/S0218348X26400281
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 15
        StartPage: 1
    Subjects:
      – SubjectFull: Lotka-Volterra equations
        Type: general
      – SubjectFull: Caputo fractional derivatives
        Type: general
      – SubjectFull: Predation
        Type: general
      – SubjectFull: Fractional calculus
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
      – SubjectFull: Stochastic analysis
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
    Titles:
      – TitleFull: THEORETICAL AND NUMERICAL ANALYSIS OF PIECEWISE LOTKA–VOLTERRA PREY–PREDATOR MODELS WITH STOCHASTIC DIFFERENTIAL OPERATORS.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: KUMAR, ATUL
      – PersonEntity:
          Name:
            NameFull: EMADIFAR, HOMAN
      – PersonEntity:
          Name:
            NameFull: ALQUDAH, MANAR
      – PersonEntity:
          Name:
            NameFull: SHAH, KAMAL
      – PersonEntity:
          Name:
            NameFull: ABDELJAWAD, THABET
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          Dates:
            – D: 01
              M: 07
              Text: 2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 0218348X
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            – Type: volume
              Value: 34
            – Type: issue
              Value: 6
          Titles:
            – TitleFull: Fractals
              Type: main
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