A reliable numerical algorithm based on an operational matrix method for treatment of a fractional order computer virus model

Jagdev Singh; Jitendra Kumar; Devendra kumar; Dumitru Baleanu; Jagdev Singh; Jitendra Kumar; Devendra kumar; Dumitru Baleanu

doi:10.3934/math.2024155

AIMS Mathematics

2024, Volume 9, Issue 2: 3195-3210. doi: 10.3934/math.2024155

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Research article

A reliable numerical algorithm based on an operational matrix method for treatment of a fractional order computer virus model

1.
Department of Mathematics, JECRC University, Jaipur, 303905, Rajasthan, India
2.
Department of Mathematics, University of Rajasthan, Jaipur, 302004, Rajasthan, India
3.
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, Lebanon
5.
Institute of Space Sciences, Magurele-Bucharest, Romania

Received: 22 October 2023 Revised: 16 November 2023 Accepted: 28 November 2023 Published: 03 January 2024
MSC : 26A33, 33C45, 65L05, 92D30

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.
- epidemiological model,
- Jacobi polynomial,
- SIRA,
- operational matrix of differentiation,
- collocation method
Citation: 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[J]. AIMS Mathematics, 2024, 9(2): 3195-3210. doi: 10.3934/math.2024155

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Abstract

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.

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