TY  - JOUR
AU  - Singh, Jagdev
AU  - Kumar, Jitendra
AU  - kumar, Devendra
AU  - Baleanu, Dumitru
PY  - 2024
TI  - A reliable numerical algorithm based on an operational matrix method for treatment of a fractional order computer virus model
JO  - AIMS Mathematics
SP  - 3195
EP  - 3210
VL  - 9
IS  - 2
AB  - 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.
UR  - https://doi.org/10.3934/math.2024155
DO  - 10.3934/math.2024155