Numerical Solutions of the SIR Mathematical Model of Computer Viruses Involving Non-linear Fractional Order Differential Equation

Authors

  • Rajratana Kamble Shri Vitthal Rukhmini College,sawana,Tq.Mahagoan,Dist.Yavatmal(M.S)
  • Pramod Kulkarni Science College,nanded(M.S)

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6693

Keywords:

Caputofractionalderivative, Fractional Differential transform method,, ,Laplace Adomian Decomposition method,, Lyapunov stability, Runge-Kutta Felhberg Method

Abstract

In this paper, the non-linear Fractional order susceptible-infected-Recovered(SIR) mathematical model of computer viruses is presented. For this Fractional differential transform method (FDTM) and the Laplace-Adomian decomposition method (LADM) are applied and compared the obtained results with Runge-Kutta Felhberg Method for γ = 1. Also, graphs of solutions are plotted up to five iterations from both the method. The fractional derivative used in the model is Caputo Fractional derivative. Using Lyapunov stability analysis,the stability verified of the given mathematical model. Solutions are obtained for three different fractional order values of γ. The validity of the result is confirmed by converting model into integer order. Errors from both the methods are compared.

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Published

2025-11-05

Issue

Vol. 18 No. 4: (October 2025)

Section

Mathematical Modeling and Numerical Analysis

License

Copyright (c) 2025 Rajratana Kamble, Pramod Kulkarni

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How to Cite

Numerical Solutions of the SIR Mathematical Model of Computer Viruses Involving Non-linear Fractional Order Differential Equation. (2025). European Journal of Pure and Applied Mathematics, 18(4), 6693. https://doi.org/10.29020/nybg.ejpam.v18i4.6693