DOI
10.34229/KCA2522-9664.25.5.6
UDC 517.9:519.6
V.M. Bulavatsky
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine,
Kyiv, Ukraine, 
v_bulav@ukr.net
V.O. Bohaienko
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine,
Kyiv, Ukraine, sevab@ukr.net
MATHEMATICAL MODELING OF FRACTIONAL-DIFFERENTIAL
DYNAMICS OF COMPUTER VIRUSES BASED ON A MODEL
WITH CAPUTO-DERIVATIVESOF PIECEWISE-CONSTANT ORDER
Abstract. A generalized fractional-differential analog with respect to the known models of the dynamics of the propagation of computer viruses, built using Caputo derivatives of piecewise-constant order, is considered. A combined technique for obtaining a numerical-analytical solution of the corresponding Cauchy problem for a nonlinear system of fractional-differential equations of piecewise-constant order has been developed. The results of qualitative analysis in relation to the conditions of correctness of this Cauchy problem, analysis of the problem’s stability according to Ulam–Hyers, and some results of computer modeling of the fractional dynamics of computer virus propagation based on this model of computer virology are presented.
Keywords: dynamics of computer virus spread, mathematical and computer modeling, fractional differential mathematical models, Caputo-derivatives of piecewise-constant order, nonlinear models, qualitative analysis, UH-stability.
full text
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