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FRACTAL–FRACTIONAL APPROACHES TO COMPUTER VIRUS CONTROL IN SCALE-FREE NETWORK STRUCTURES.

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Title: FRACTAL–FRACTIONAL APPROACHES TO COMPUTER VIRUS CONTROL IN SCALE-FREE NETWORK STRUCTURES.
Authors: ALHAZMI, MUFLIH1 (AUTHOR) Muflih.alhazmi@nbu.edu.sa, SABER, SAYED2,3 (AUTHOR) Sayed011258@science.bsu.edu.eg
Source: Fractals. 2026, Vol. 34 Issue 6, p1-16. 16p.
Subjects: Scale-free network (Statistical physics), Caputo fractional derivatives, Computer virus prevention, Fixed point theory, Computer simulation, Mathematical models, Stability theory
Abstract: This study develops a novel fractal–fractional (FF) model using the Caputo derivative to describe computer virus propagation dynamics in networked environments. The model incorporates memory effects and fractal geometry to accurately simulate virus transmission across complex networks. Fixed-point theory establishes solutions' existence and uniqueness, while stability analysis ensures robustness. Numerical simulations demonstrate the efficacy of targeted interventions, such as antivirus deployment in high-degree network hubs. The proposed framework highlights the potential of FF derivatives for enhancing our understanding of virus dynamics and informing control strategies. This work bridges a critical gap in the study of computer viruses using fractal and fractional calculus. It provides tools for robust analysis and mitigation in interconnected systems. [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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Header DbId: egs
DbLabel: Engineering Source
An: 194008154
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: FRACTAL–FRACTIONAL APPROACHES TO COMPUTER VIRUS CONTROL IN SCALE-FREE NETWORK STRUCTURES.
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  Data: <searchLink fieldCode="AR" term="%22ALHAZMI%2C+MUFLIH%22">ALHAZMI, MUFLIH</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> Muflih.alhazmi@nbu.edu.sa</i><br /><searchLink fieldCode="AR" term="%22SABER%2C+SAYED%22">SABER, SAYED</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<i> Sayed011258@science.bsu.edu.eg</i>
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  Data: <searchLink fieldCode="JN" term="%22Fractals%22">Fractals</searchLink>. 2026, Vol. 34 Issue 6, p1-16. 16p.
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  Data: <searchLink fieldCode="DE" term="%22Scale-free+network+%28Statistical+physics%29%22">Scale-free network (Statistical physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Caputo+fractional+derivatives%22">Caputo fractional derivatives</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+virus+prevention%22">Computer virus prevention</searchLink><br /><searchLink fieldCode="DE" term="%22Fixed+point+theory%22">Fixed point theory</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This study develops a novel fractal–fractional (FF) model using the Caputo derivative to describe computer virus propagation dynamics in networked environments. The model incorporates memory effects and fractal geometry to accurately simulate virus transmission across complex networks. Fixed-point theory establishes solutions' existence and uniqueness, while stability analysis ensures robustness. Numerical simulations demonstrate the efficacy of targeted interventions, such as antivirus deployment in high-degree network hubs. The proposed framework highlights the potential of FF derivatives for enhancing our understanding of virus dynamics and informing control strategies. This work bridges a critical gap in the study of computer viruses using fractal and fractional calculus. It provides tools for robust analysis and mitigation in interconnected systems. [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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      – Type: doi
        Value: 10.1142/S0218348X2640044X
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 16
        StartPage: 1
    Subjects:
      – SubjectFull: Scale-free network (Statistical physics)
        Type: general
      – SubjectFull: Caputo fractional derivatives
        Type: general
      – SubjectFull: Computer virus prevention
        Type: general
      – SubjectFull: Fixed point theory
        Type: general
      – SubjectFull: Computer simulation
        Type: general
      – SubjectFull: Mathematical models
        Type: general
      – SubjectFull: Stability theory
        Type: general
    Titles:
      – TitleFull: FRACTAL–FRACTIONAL APPROACHES TO COMPUTER VIRUS CONTROL IN SCALE-FREE NETWORK STRUCTURES.
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            NameFull: ALHAZMI, MUFLIH
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            NameFull: SABER, SAYED
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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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              Value: 34
            – Type: issue
              Value: 6
          Titles:
            – TitleFull: Fractals
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