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A hybrid analytical scheme for the numerical computation of time fractional computer virus propagation model and its stability analysis

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  • Dubey, Ved Prakash
  • Kumar, Rajnesh
  • Kumar, Devendra

Abstract

In this paper, we present an application of the homotopy perturbation transform method to compute the approximate analytical solution of the nonlinear fractional order computer virus propagation (CVP) model. The fractional derivatives are used in Caputo sense. The proposed approximate method generates the numerical solution in the shape of a rapid convergent series by utilizing the provided initial conditions. The main purpose of the paper is to analyze the effect of variation of fractional order α on the meeting time of susceptible, infected and recovered computers. Moreover, the local stability analysis of the fractional order computer virus model is also presented using Routh–Hurwitz stability criterion.

Suggested Citation

  • Dubey, Ved Prakash & Kumar, Rajnesh & Kumar, Devendra, 2020. "A hybrid analytical scheme for the numerical computation of time fractional computer virus propagation model and its stability analysis," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
  • Handle: RePEc:eee:chsofr:v:133:y:2020:i:c:s0960077920300254
    DOI: 10.1016/j.chaos.2020.109626
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    1. Suheil A. Khuri, 2001. "A Laplace decomposition algorithm applied to a class of nonlinear differential equations," Journal of Applied Mathematics, Hindawi, vol. 1, pages 1-15, January.
    2. Jianguo Ren & Yonghong Xu & Yongchang Zhang & Yongquan Dong & Guosheng Hao, 2012. "Dynamics of a Delay-Varying Computer Virus Propagation Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-12, August.
    3. Song, Li-Peng & Jin, Zhen & Sun, Gui-Quan, 2011. "Modeling and analyzing of botnet interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 347-358.
    4. Ghorbani, Asghar, 2009. "Beyond Adomian polynomials: He polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1486-1492.
    5. Ren, Jianguo & Yang, Xiaofan & Yang, Lu-Xing & Xu, Yonghong & Yang, Fanzhou, 2012. "A delayed computer virus propagation model and its dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 74-79.
    6. Abbasbandy, S., 2007. "A numerical solution of Blasius equation by Adomian’s decomposition method and comparison with homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 257-260.
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    Cited by:

    1. Singh, Harendra & Baleanu, Dumitru & Singh, Jagdev & Dutta, Hemen, 2021. "Computational study of fractional order smoking model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

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