801
Views
0
CrossRef citations to date
0
Altmetric
Research Article

A fractional-order model for computer viruses and some solution associated with residual power series method

, , , &
Article: 2214301 | Received 05 Sep 2022, Accepted 21 Feb 2023, Published online: 03 Aug 2023

References

  • Kumar S. A new fractional modeling arising in engineering sciences and its analytical approximate solution. Alex Eng J. 2013;52(4):813–819.
  • Kilbas A, Srivastava H, Trujillo J. Theory and applications of fractional differential equations. Amsterdam: Elsevier; 2006.
  • Al-Smadi M, Djeddi N, Momani S, et al. An attractive numerical algorithm for solving nonlinear Caputo–Fabrizio fractional Abel differential equation in a Hilbert space. Adv Differ Equ. 2021;2021(1):271.
  • Al-Smadi M, Abu Arqub O, Zeidan D. Fuzzy fractional differential equations under the Mittag–Leffler kernel differential operator of the ABC approach: theorems and applications. Chaos Solitons Fractals. 2021;146:Article ID 110891.
  • Al-Smadi M. Simplified iterative reproducing kernel method for handling time-fractional BVPs with error estimation. Ain Shams Eng J. 2018;9(4):2517–2525.
  • Hasan S, Al-Smadi M, El-Ajou A, et al. Numerical approach in the Hilbert space to solve a fuzzy Atangana–Baleanu fractional hybrid system. Chaos Solitons Fractals. 2021;143:Article ID 110506.
  • Abuteen E, Freihat A, Al-Smadi M, et al. Approximate series solution of nonlinear, fractional Klein–Gordon equations using fractional reduced differential transform method. J Math Stat. 2016;12(1):23–33.
  • Al-Smadi M, Freihat A, Khalil H, et al. Numerical multistep approach for solving fractional partial differential equations. Int J Comput Methods. 2021;14(3):Article ID 1750029.
  • Moaddy K, Freihat A, Al-Smadi M, et al. Numerical investigation for handling fractional-order Rabinovich–Fabrikant model using the multistep approach. Soft Comput. 2018;22(3):773–782.
  • Al-Smadi M, Abu Arqub O. Computational algorithm for solving Fredholm time-fractional partial integrodifferential equations of Dirichlet functions type with error estimates. Appl Math Comput. 2019;342:280–294.
  • Al-Smadi M, Freihat A, Abu Hammad M, et al. Analytical approximations of partial differential equations of fractional order with multistep approach. J Comput Theor Nanosci. 2016;13(11):7793–7801.
  • Alabedalhadi M, Al-Smadi M, Al-Omari S, et al. Structure of optical soliton solution for nonlinear resonant space–time Schrdinger equation in conformable sense with full nonlinearity term. Phys Scr. 2020;95(10):Article ID 105215.
  • Al-Smadi M, Dutta H, Hasan S, et al. On numerical approximation of Atangana–Baleanu–Caputo fractional integro-differential equations under uncertainty in Hilbert space. Math Model Nat Phenom. 2021;16:41.
  • Al-Smadi M, Abu Arqub O, Hadid S. An attractive analytical technique for coupled system of fractional partial differential equations in shallow water waves with conformable derivative. Commun Theor Phys. 2020;72(8):Article ID 085001.
  • Al-Smadi M, Abu Arqub O, Hadid S. Approximate solutions of nonlinear fractional Kundu–Eckhaus and coupled fractional massive Thirring equations emerging in quantum field theory using conformable residual power series method. Phys Scr. 2020;95(10):Article ID 105205.
  • Murray W. The application of epidemiology to computer viruses. Comput Secur. 1988;7(2):139–145.
  • Gleissner W. A mathematical theory for the spread of computer viruses. Comput Secur. 1989;8(1):35–41.
  • Kephart JO, White SR. Directed-graph epidemiological models of computer viruses. In: Proceedings of the IEEE symposium on security and privacy, USA; 1991. p. 343–359.
  • Kephart JO, White SR. Measuring and modelling computer virus prevalence. In: Proceedings of the IEEE symposium on security and privacy; 1993. p. 2–15.
  • Kephart JO, White SR, Chess DM. Computers and epidemiology. J Mag. 1993;5:20–26.
  • Kephart JO, Sorkin GB, Chess DM, et al. Fighting computer viruses. Sci Am. 1997;277:88–93.
  • Huang CY, Lee CL, Wen TH, et al. A computer virus spreading model based on resource limitations and interaction costs. J Syst Softw. 2013;86(3):801–808.
  • Hasan S, Al-Zoubi A, Freihet A, et al. Solution of fractional SIR epidemic model using residual power series method. Appl Math Inf Sci. 2019;13(2):153–161.
  • Freihat AA, Handam AH. Solution of the SIR models of epidemics using MSGDTM. Appl Appl Math. 2014;9(2):622–636.
  • Piqueira JRC, Araujo VO. A modified epidemiological model for computer viruses. Appl Math Comput. 2009;213(2):355–360.
  • Freihat A, Zurigat M, Handam A. The multi-step homotopy analysis method for modified epidemiological model for computer viruses. Afr Mat. 2015;26(3–4):585–596.
  • Lefebvre M. A stochastic model for computer virus propagation. J Dyn Games. 2020;7(2):163.
  • Kumar D, Singh J. New aspects of fractional epidemiological model for computer viruses with Mittag–Leffler law. Math Model Health Soc Appl Sci. 2020;39:283–301.
  • Upadhyay RK, Singh P. Modeling and control of computer virus attack on a targeted network. Phys A: Stat Mech Appl. 2020;538:Article ID 122617.
  • Tang W, Liu Y-J, Chen Y-L, et al. SLBRS: network virus propagation model based on safety entropy. Appl Soft Comput. 2020;97:Article ID 106784.
  • Al-Smadi M, Abu Arqub O, Momani S. A computational method for two-point boundary value problems of fourth-order mixed integrodifferential equations. Math Probl Eng. 2013;2013:Article ID 832074.
  • Han X, Tan Q. Dynamical behavior of computer virus on internet. Appl Math Comput. 2010;217(6):2520–2526.
  • Baleanu D, Abadi M, Jajarmi A, et al. A new comparative study on the general fractional model of COVID-19 with isolation and quarantine effects. Alex Eng J. 2022;61(6):4779–4791.
  • Baleanu D, Ghassabzade F, Nieto J, et al. On a new and generalized fractional model for a real cholera outbreak. Alex Eng J. 2022;61(11):9175–9186.
  • Erturk V, Godwe E, Baleanu D, et al. Novel fractional-order Lagrangian to describe motion of beam on nanowire. Acta Phys Pol. 2022;140(3):265–272.
  • Agarwal P, Nieto J, Ruzhansky M, et al. Analysis of infectious disease problems (Covid-19) and their global impact. Singapore: Springer; 2021.
  • El-Ajou A, Abu Arqub O, Al-Smadi M. A general form of the generalized Taylors formula with some applications. Appl Math Comput. 2015;256:851–859.
  • Kumar S, Ahmadian A, Kumar R, et al. An efficient numerical method for fractional SIR epidemic model of infectious disease by using Bernstein wavelets. Mathematics. 2020;8(4):558.
  • Farman M, Ahmad A, Akgl A, et al. Epidemiological analysis of the coronavirus disease outbreak with random effects. Comput Mater Contin. 2021;67(3):3215–3227.
  • Komashynska I, Al-Smadi M, Abu Arqub O, et al. An efficient analytical method for solving singular initial value problems of nonlinear systems. Appl Math Inf Sci. 2016;10(2):647–656.
  • Al-Smadi M, Abu Arqub O, El-Ajou A. A numerical iterative method for solving systems of first-order periodic boundary value problems. J Appl Math. 2014;2014:Article ID 135465.
  • Chen J, Hu M-B, Li M. Traffic-driven epidemic spreading in multiplex networks. Phys Rev E. 2020;101:Article ID 012301.
  • Al-Jarrah A, Massa'deh MO, Baareh AEK, et al. A study on r-edge regular intuitionistic fuzzy graphs. J Math Comput Sci. 2021;23(4):279–288.