A reliable numerical algorithm based on an operational matrix method for treatment of a fractional order computer virus model
A computer network can detect potential viruses through the use of kill signals, thereby minimizing the risk of virus propagation. In the realm of computer security and defensive strategies, computer viruses play a significant role. Understanding of their spread and extension is a crucial component....
Main Authors: | , , , |
---|---|
Format: | Article |
Language: | English |
Published: |
AIMS Press
2024-01-01
|
Series: | AIMS Mathematics |
Subjects: | |
Online Access: | https://aimspress.com/article/doi/10.3934/math.2024155?viewType=HTML |
_version_ | 1797348704990003200 |
---|---|
author | Jagdev Singh Jitendra Kumar Devendra kumar Dumitru Baleanu |
author_facet | Jagdev Singh Jitendra Kumar Devendra kumar Dumitru Baleanu |
author_sort | Jagdev Singh |
collection | DOAJ |
description | A computer network can detect potential viruses through the use of kill signals, thereby minimizing the risk of virus propagation. In the realm of computer security and defensive strategies, computer viruses play a significant role. Understanding of their spread and extension is a crucial component. To address this issue of computer virus spread, we employ a fractional epidemiological SIRA model by utilizing the Caputo derivative. To solve the fractional-order computer virus model, we employ a computational technique known as the Jacobi collocation operational matrix method. This operational matrix transforms the problem of arbitrary order into a system of nonlinear algebraic equations. To analyze this system of arbitrary order, we derive an approximate solution for the fractional computer virus model, also considering the Vieta Lucas polynomials. Numerical simulations are performed and graphical representations are provided to illustrate the impact of order of the fractional derivative on different profiles. |
first_indexed | 2024-03-08T12:09:49Z |
format | Article |
id | doaj.art-9541ea7e82db45b790924e7b024d8bd1 |
institution | Directory Open Access Journal |
issn | 2473-6988 |
language | English |
last_indexed | 2024-03-08T12:09:49Z |
publishDate | 2024-01-01 |
publisher | AIMS Press |
record_format | Article |
series | AIMS Mathematics |
spelling | doaj.art-9541ea7e82db45b790924e7b024d8bd12024-01-23T01:25:12ZengAIMS PressAIMS Mathematics2473-69882024-01-01923195321010.3934/math.2024155A reliable numerical algorithm based on an operational matrix method for treatment of a fractional order computer virus modelJagdev Singh0Jitendra Kumar1Devendra kumar 2Dumitru Baleanu31. Department of Mathematics, JECRC University, Jaipur, 303905, Rajasthan, India3. Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, 02447, Korea 4. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon1. Department of Mathematics, JECRC University, Jaipur, 303905, Rajasthan, India2. Department of Mathematics, University of Rajasthan, Jaipur, 302004, Rajasthan, India4. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon4. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon 5. Institute of Space Sciences, Magurele-Bucharest, RomaniaA computer network can detect potential viruses through the use of kill signals, thereby minimizing the risk of virus propagation. In the realm of computer security and defensive strategies, computer viruses play a significant role. Understanding of their spread and extension is a crucial component. To address this issue of computer virus spread, we employ a fractional epidemiological SIRA model by utilizing the Caputo derivative. To solve the fractional-order computer virus model, we employ a computational technique known as the Jacobi collocation operational matrix method. This operational matrix transforms the problem of arbitrary order into a system of nonlinear algebraic equations. To analyze this system of arbitrary order, we derive an approximate solution for the fractional computer virus model, also considering the Vieta Lucas polynomials. Numerical simulations are performed and graphical representations are provided to illustrate the impact of order of the fractional derivative on different profiles.https://aimspress.com/article/doi/10.3934/math.2024155?viewType=HTMLepidemiological modeljacobi polynomialsiraoperational matrix of differentiationcollocation method |
spellingShingle | Jagdev Singh Jitendra Kumar Devendra kumar Dumitru Baleanu A reliable numerical algorithm based on an operational matrix method for treatment of a fractional order computer virus model AIMS Mathematics epidemiological model jacobi polynomial sira operational matrix of differentiation collocation method |
title | A reliable numerical algorithm based on an operational matrix method for treatment of a fractional order computer virus model |
title_full | A reliable numerical algorithm based on an operational matrix method for treatment of a fractional order computer virus model |
title_fullStr | A reliable numerical algorithm based on an operational matrix method for treatment of a fractional order computer virus model |
title_full_unstemmed | A reliable numerical algorithm based on an operational matrix method for treatment of a fractional order computer virus model |
title_short | A reliable numerical algorithm based on an operational matrix method for treatment of a fractional order computer virus model |
title_sort | reliable numerical algorithm based on an operational matrix method for treatment of a fractional order computer virus model |
topic | epidemiological model jacobi polynomial sira operational matrix of differentiation collocation method |
url | https://aimspress.com/article/doi/10.3934/math.2024155?viewType=HTML |
work_keys_str_mv | AT jagdevsingh areliablenumericalalgorithmbasedonanoperationalmatrixmethodfortreatmentofafractionalordercomputervirusmodel AT jitendrakumar areliablenumericalalgorithmbasedonanoperationalmatrixmethodfortreatmentofafractionalordercomputervirusmodel AT devendrakumar areliablenumericalalgorithmbasedonanoperationalmatrixmethodfortreatmentofafractionalordercomputervirusmodel AT dumitrubaleanu areliablenumericalalgorithmbasedonanoperationalmatrixmethodfortreatmentofafractionalordercomputervirusmodel AT jagdevsingh reliablenumericalalgorithmbasedonanoperationalmatrixmethodfortreatmentofafractionalordercomputervirusmodel AT jitendrakumar reliablenumericalalgorithmbasedonanoperationalmatrixmethodfortreatmentofafractionalordercomputervirusmodel AT devendrakumar reliablenumericalalgorithmbasedonanoperationalmatrixmethodfortreatmentofafractionalordercomputervirusmodel AT dumitrubaleanu reliablenumericalalgorithmbasedonanoperationalmatrixmethodfortreatmentofafractionalordercomputervirusmodel |