Про один підхід до застосування дробового аналізу для моделювання процесів інформаційного поширення
The article discusses a technique for constructing a model and a method for finding solutions in the problem of imitating the process of information dissemination based on the use of a boundary value problem for a fractional differential equation in partial derivatives. It is proposed to use the ana...
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The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
2021
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Репозитарії
System research and information technologies| _version_ | 1866302728590852096 |
|---|---|
| author | Ivokhin, Eugene Adzhubey, Larisa Naumenko, Yuriy Makhno, Mykhailo |
| author_facet | Ivokhin, Eugene Adzhubey, Larisa Naumenko, Yuriy Makhno, Mykhailo |
| author_sort | Ivokhin, Eugene |
| baseUrl_str | http://journal.iasa.kpi.ua/oai |
| collection | OJS |
| datestamp_date | 2022-06-20T14:19:48Z |
| description | The article discusses a technique for constructing a model and a method for finding solutions in the problem of imitating the process of information dissemination based on the use of a boundary value problem for a fractional differential equation in partial derivatives. It is proposed to use the analogy technique for modeling information dissemination processes, which is based on the use of the features of a fractional analysis and the diffuse nature of information penetration processes. A method for constructing hybrid models is proposed, which makes it possible to take into account changes in the interval of values of the spatial variable over time. Homogeneous and inhomogeneous models of diffusion processes are considered, which make it possible to numerically obtain and analyze experimental data for solving problems of monitoring the levels of information dissemination in social groups. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2021.4.10 |
| first_indexed | 2025-07-17T10:27:11Z |
| format | Article |
| fulltext |
E.V. Ivokhin, L.T. Adzhubey, Yu.A. Naumenko, M.F. Makhno, 2021
128 ISSN 1681–6048 System Research & Information Technologies, 2021, № 4
UDC 004.942:519.876.5
DOI: 10.20535/SRIT.2308-8893.2021.4.10
ON ONE APPROACH TO USING OF FRACTIONAL ANALYSIS
FOR HYBRID MODELING OF INFORMATION
DISTRIBUTION PROCESSES
E.V. IVOKHIN, L.T. ADZHUBEY, YU.A. NAUMENKO, M.F. MAKHNO
Abstract. The article discusses a technique for constructing a model and a method
for finding solutions in the problem of imitating the process of information
dissemination based on the use of a boundary value problem for a fractional
differential equation in partial derivatives. It is proposed to use the analogy
technique for modeling information dissemination processes, which is based on the
use of the features of a fractional analysis and the diffuse nature of information
penetration processes. A method for constructing hybrid models is proposed, which
makes it possible to take into account changes in the interval of values of the spatial
variable over time. Homogeneous and inhomogeneous models of diffusion processes
are considered, which make it possible to numerically obtain and analyze
experimental data for solving problems of monitoring the levels of information
dissemination in social groups.
Keywords: information, dissemination, modeling, diffusion hybrid models,
fractional analysis.
INTRODUCTION
The study of real processes and phenomena by methods of mathematical
modeling using a strictly deterministic approach is associated with significant
limitations. In many cases, the systems and processes under consideration possess
unusual properties of fractality due to the complex geometric structure of
the surface, self-similarity of sets and media, inhomogeneity of dynamic
characteristics, and the presence of the effect of heredity. The theory of fractals
has found application in describing the geometric properties of complex objects,
in the analysis and forecasting of the behavior of dynamic systems and processes.
At the same time, to simulate the dynamics of processes and phenomena in fractal
systems, one often resorts to the apparatus of fractional-differential calculus.
A fractional derivative with respect to time is used to indicate that a given process
has memory, and a fractional derivative with respect to a coordinate is used to
indicate that the process takes place in a self-similar inhomogeneous medium.
The processes of heating solids in non-equilibrium conditions or the diffusion of
impurities in the soil, the spread of heat in highly porous media also have
properties inherent in fractals. For example, work [1] describes a fractional
differential approach for modeling a wide class of problems in the theory of heat
and mass transfer: heat transfer in inert media, isothermal processes of mass
transfer, mass transfer at the contact boundary of moving media, heat transfer in
the presence of nonlinear heat release. In [2], a mathematical model of anomalous
diffusion is presented in the form of a partial differential equation of mixed order.
The work [3] describes a model of systems with memory, provides a
mathematical formalization of the work of real elements of electrical circuits. In
On one approach to using of fractional analysis for hybrid modeling of information …
Системні дослідження та інформаційні технології, 2021, № 4 129
work [4], generalized equations of diffusion and drift of charge carriers in
disordered semiconductors for dispersive transfer were obtained. Unfortunately,
not all differential equations with fractional derivatives can be solved on the basis
of analytical methods and approaches, since they are developed for a limited class
of problems. In this case, numerical solution methods are used more often [5, 6].
Despite the problems of use, modern research on modeling problems is often
based on the use of fractional analysis and its intensive implementation for
solving problems in various fields of knowledge. Using fractional integro-
differentiation or fractional analysis, one can write out adequate mathematical
models of social, natural, economic and other processes [7]. In accordance with
the new interpretation of the experimental data, the model parameters make it
possible to more accurately approximate the obtained data and provide
information on the properties of the research object based on the solutions of the
corresponding nonlocal equations. It should be noted that the use of differential
equations of fractional order, on the one hand, leads to the need to solve an
infinite number of differential equations, and, on the other hand, allows one to
obtain a set of solutions corresponding to them and to consider various functional
spaces. This diversity also allows to improve the adequacy of mathematical
models. The problems of formalizing and studying the development in time of the
processes of information dissemination and influence on society are one of the
most important, requiring the use of a fundamentally new toolkit, which should
allow to adequately reflect the state of the dynamic component of the information
dissemination process [8].
At the same time, when developing new approaches, the adaptation of
classical methods of analysis and processing of dynamic processes is often used,
which is based on the use of the analogy method [9–11]. It is obvious that the
dissemination of information in society, thoughts about social networks,
advertising products and other information processes are in many ways similar to
the processes of distribution (penetration) of a substance that spreads in a certain
environment. It is assumed that the environment is homogeneous and the area of
admissible distribution of information can be calculated based on the structural
extension of the basic model by a hybrid subsystem [9]. This hybrid model turned
out to be quite effective for describing the states of various target groups of
people affected by the information flow [11].
FORMALIZATION OF THE INFORMATION DISSEMINATION PROCESS
BASED ON HYBRID DIFFUSION MODELS
One of the approaches, within the framework of which both the classical and
the system method of modeling the behavior of objects (systems) is effectively
implemented, is a method based on the application of formal (biological, chemical
or physical) analogies in the process of dynamics formalizing [8, 9, 12]. The
practical application of the analogy method begins with the development of the
first approximation of the model and consists in converting the mechanistic
analogue to the mathematical model of the process under study. The next stage
involves the use of mathematical tools to analyze the model. The mathematical
results obtained in the process of computational experiments go through the
subsequent stage of reverse interpretation in terms of the analogy system. And
finally, it is necessary to evaluate the results obtained on the basis of the model in
order to decide whether they are satisfactory — formally substantiated and
sufficient to achieve the goals.
E.V. Ivokhin, L.T. Adzhubey, Yu.A. Naumenko, M.F. Makhno
ISSN 1681–6048 System Research & Information Technologies, 2021, № 4 130
The tasks of the analytical processing of modern information flows and their
influence require solving the problems of studying the dynamics of information
dissemination processes based on simulation and forecasting tools. The
development of models and methods for simulating information impacts, taking
into account the processes of information dynamics, can effectively solve
important communication problems, significantly increase the level of
information security of the state, and tactically and strategically predict the
development of information confrontation events. A constructive method for
analyzing the dynamics of information dissemination processes can be proposed
based on the use of a fundamentally new toolkit using the method of analogy and
hybrid models, which allows adequately reflecting the state of the dynamic
component of the process of disseminating information [10, 11, 13–17].
We will model changes in the level (concentration) of information in a popu-
lation with the help of the diffusion equation [18], assuming that this process is
similar to the spread of a substance (infection) over a specific time period
],0[ Tt and can be described by a scalar equation with Kaputo–Gerasimov
fractional derivative [18] of order , 10 ,
2
2
0
).()(),(
x
txutktxuD t
, (1)
where
z
t ds
sz
sf
dz
dzfD
0
0 )(
)(
)1(
1)( ,
0
1)( dsesv sv — gamma-
function, with boundary conditions in the form )(),0( 0 tutuх , 0)(0 tu —
given function, 0),1( tих , ],0[ Tt , and initial condition 0)0,( xu , 10 x ,
)()(0
0 tftfD t .
We believe that the contingent of the target population is formed of
3 subgroups based on the perception of information. We identify the part of the
population that is sensitive to the influence of information )(1 ty , the part which is
already under the influence of information )(2 ty and the part which is indifferent
to information influence )(3 ty . Then, using the Bailey model [19], the dissemina-
tion of appearance information:
)()()( 211 tytyty ;
)()()()( 2212 tytytyty ; (2)
)()( 23 tyty ,
with the initial condition ;)0(;)0( 0
22
0
11 yyyy 0
33 )0( yy , where the total of
cure and disease rates are considered to be 1, )()( 21 tyty )(3 ty =1, 0t , there
a system of differential equations that describes the process of information dis-
semination in the target population can be written. Their solutions determine the
dynamics of the rate values of individual subgroups.
With such assumptions, the maximum threshold value of x , 1)(0 tx ,
will depend on the time, so we have )(0 txx , )()()( 21 tytytx , where
)(1 ty , )(2 ty — are the components of the solution of system (2).
On one approach to using of fractional analysis for hybrid modeling of information …
Системні дослідження та інформаційні технології, 2021, № 4 131
MODELING OF INFORMATION DISTRIBUTION PROCESSES
(HOMOGENEOUS DIFFUSION)
The applied study of the obtained model (1) – (2) in the general case is very
complex. In order to analyze the constructiveness of the proposed approach, we
consider some partial cases. Assume that the level of information dissemination in
the group is initially zero. After that, the members of the group have some
external influence of information content, which at any time ],0[ Tt is
characterized by a constant speed 0)(),0( 0 tutuх .
Given the cumulative nature of the information dissemination process in so-
ciety, we will search for a partial solution of the diffusion equation (1) in the form
),( txu = atdX
x
0
)( , (3)
where the parameter а for the impact over time for each point in time t is con-
sidered proportional to the rate of change of magnitude )(tx , i.e. а )(tx ,
0 .
To find solutions, we will assume that the instantaneous value of the
coefficient of information penetration )(tk will be proportional to the rate of
change of the part of the population that is considered to be susceptible to the
influence of external information, i.e.
)(tk )(tx , 0 .
It is impossible to obtain an analytical form of the Kaputo–Gerasimov
fractional derivative, which is written in the left part of equation (1), for an
arbitrarily given function ),( txu . However, to find the value of the derivative,
you can use different numerical methods [18]. In our case, to study the solutions
of the diffusion equation, we consider a partial case for which a fractional
derivative can be calculated.
It is easy to verify that tD t0
0 2/1
/1
)1()1(
1
ds
s
s
, where the
improper integral coincides on the basis of comparison )1( /1* sO , 10 ,
i.e. the fractional derivative has a finite value, the diffusion equation (1) is correct
and has a solution for arbitrary , 10 .
Let 5,0 . Then, omitting the cumbersome details of transformations and
substitutions and taking into account that )5,0( , we obtain the value of the
fractional derivative 2/2/12/1
0 tD t .
Taking into account the assumptions made about the solution, we will
rewrite the boundary conditions of model (1) in the form ),0( tuх
)()2( tx , 0),( tхих , 1)( хtx , ],0[ Tt .
It is clear that in this formulation, diffusion equation (1) has a special solu-
tion that can be obtained provided ctx )( , c some constant, ]1,0[c . In other
words, with the presence of a stationary process in the dynamics of the size of the
contingent under the influence of information, the level of information dissemina-
tion in the group remains constant. This solution is trivial.
E.V. Ivokhin, L.T. Adzhubey, Yu.A. Naumenko, M.F. Makhno
ISSN 1681–6048 System Research & Information Technologies, 2021, № 4 132
Supposing that 0)( tx we have that at any given time ],0[ Tt the
diffusion equation has a partial solution of the form (3), for which the next
ordinary first-order differential equation must be solved
)2()( dxxdX ,
with the initial condition at the end of the interval 0))(( txX . The solution of
this equation will be the function ))((2)( xtxxX , )(0 txx , for
which the value ))((2)0( txX is corresponding to the first boundary
condition of the diffusion equation.
So, finally, for the arbitrary 0 and 0 equation (1) with the fractional
derivative for 5,0 has the solution of the form
),( txu = ))()2)((2( 2/1ttxxxtx ,
which at any time ],0[ Tt determines the level of distribution of information
within a subgroup )(0 txx , the size of which is a fraction )(tx of the total
number of members of the group calculated by the system solutions (2) (below the
values )(tx , )(tx we consider the instantaneous values of magnitude )(tх
)()( 21 tyty and its velocity which is obtained from (2) at any moment of time t ).
This solution may be generalized. It follows from the initial conditions of
system (2) that 1)0( x . This allows you to rewrite the layout of the solution
),( txu subject to the initial condition 0)0,( xu , 10 x from diffusion
equation (1).
Indeed, the function
),( txu = ))(1())()2)((2( txttxxxtxx ,
satisfies equation (1) and the initial and boundary conditions, which makes it pos-
sible to consider it as a general solution of the diffusion equation (1) for 5,0 .
Fig. 1 shows examples of spatio-temporal distribution of levels of
information perception within a given target group, which is calculated on the
Fig 1. Distribution of levels of perception of information in the target group over time
(coefficients ;1,0 2,0 )
The behavior of the solution of the diffusion
equation (excluding the factor (1-xг))
The behavior of the solution of the diffusion
equation (taking into account the factor (1-xг))
x
u(
t,x
)
0,4
0,35
0,3
0,25
0,2
0,15
0,1
0,05
0
0,1
0,08
0,06
0,04
0,02
0
u(
t,x
)
x
t t
On one approach to using of fractional analysis for hybrid modeling of information …
Системні дослідження та інформаційні технології, 2021, № 4 133
basis of a hybrid model (1)–(2), obtained by diffusion equation (1) with a
fractional derivative Kaputo–Gerasimov order 5,0 and use of the system (2).
MODELING OF INFORMATION DISTRIBUTION PROCESSES
(INHOMOGENEOUS DIFFUSION)
It is clear that this approach can be extended to the case of inhomogeneous
diffusion equations. For example, we can consider a generalization of the model
proposed in [14], which examines the case of diffusion in an environment that is
under external information and which changes over time (for example, in the form
of group attitudes to the quality or content of information). In this case, it is said
that such an environment “moves” at a constant speed, which is also assumed to
be proportional to the change in the number of covered members of the group.
This assumption is quite acceptable if we assume a low (which can be neglected)
level of intragroup information exchange and consider as the main factor the
external influence on the level of information dissemination in the target group. In
this case, the diffusion process must satisfy Nernst’s law [20], according to which
the model has the form
)()()(),( 22
0 xuxutktxuD t . (4)
Here is the velocity of the medium,
1))((exp5,0),0( txtuх ,
0),( txих , 1)( хtx , ],0[ Tt . Based on this law, the level of information
(concentration) ),( txq that penetrates from the external environment can be
calculated based on the interrelations xutxq ),( , )(tx , 10 .
Put, as in the previous case, 5,0 . Writing the partial solution of the
inhomogeneous diffusion equation (4) in the form (3) for each moment of time
],0[ Tt , we obtain an inhomogeneous first-order differential equation
)()()()()(5,0 хХtxхХtxtx , (5)
in which the value )(tx is considered as the instantaneous value of the rate of
change of the value )(tх , which can be obtained from (2) for each time t .
Assuming that 0)( tx , equation (5) can be rewritten as
5,0)()( хХxX ,
with the initial condition at the end of interval in form 0))(( txX .
The solution to this equation is a function
5,0)(хX
)1)))((((exp хtx , from where we obtain a relationship )0(X
. )1)))((((exp5,0
хtx , that meets the first boundary condition of
the inhomogeneous diffusion equation (4).
Thus, applying model (4) to describe the process of information propagation
in the conditions of external information influence, which changes over time, for
arbitrary 0 , 0 , 0 , we obtain the solution of equation (4):
E.V. Ivokhin, L.T. Adzhubey, Yu.A. Naumenko, M.F. Makhno
ISSN 1681–6048 System Research & Information Technologies, 2021, № 4 134
2/12 )(5,0))(exp1())((exp)(5,0),( ttxxxtxtxu
,
that to provide the initial condition can be generalized in the form
))()2())(exp1())(exp()2((),( 2 ttxxtxtxu ,
))(1( tx ,
and which at any time ],0[ Tt determines the level of distribution of information
within a subgroup )(0 txx , the size of which is a fraction )(tx of the total
number of group members, calculated using the solutions of the system (2).
Fig. 2 shows examples of the distribution of levels of information impact in the
target group, calculated on the basis of solutions of the diffusion model of the form (4).
CONCLUSIONS
This paper proposes an approach to the construction of hybrid mathematical mod-
els of the dynamics of information processes propagation in the target population,
taking into account and without taking into account the impact on the process of
information dissemination by external sources and other means.
Formalization is based on the idea of using hybrid mathematical models,
which consist of the diffusion (penetration) equation based on a fractional
differential equation in partial derivatives and dynamic models, that describe the
processes of change in the size of the contingent of the information dissemination
environment. A scalar solution for a one-dimensional representation of a group
contingent is considered. Various cases of formalization of external influence on
the process of information dissemination are considered.
Examples of numerical experiments to evaluate the level of impact based on
the application of this approach are given, and their results are analyzed. The
comparative analysis allows to confirm the existence of sufficient adequacy of
model data and data obtained as a result of real observations of the processes of
change in the perception of information within specific target population groups.
The scientific novelty of obtained results is that the proposed technique
allows us to describe the levels of propagation, influence and storage of
information in a group on the basis of the solution of the diffusion equation, the
0,4
0,35
0,3
0,25
0,2
0,15
0,1
0,05
0
u(
t,x
)
0,016
0,014
0,012
0,010
0,008
0,006
0,04
0,02
0
u(
t,x
)
x x
t t
The behavior of the solution of the diffusion
equation (excluding the factor )1( x )
The behavior of the solution of the diffusion
equation (taking into account the factor )1( x )
Fig. 2. Distribution of levels of perception of information, which changes in time, in the
target group with the external information influence (coefficients of proportionality
,1,0 2,0 , 2,0 )
On one approach to using of fractional analysis for hybrid modeling of information …
Системні дослідження та інформаційні технології, 2021, № 4 135
variation of the propagation intervals in which is determined by the additional
relationships obtained from the solutions of the additional differential equation
(for example, Bailey model (2)).
The practical significance of obtained results is that the proposed
methodology form the basis for the development of the applied research project
for the analysis of the distribution processes and the influence of information
flows in social networks. The development of methods and approaches to support
decision making in this direction is an important task that have being solved with
the aim of testing concepts and technological solutions in the field of constructive
assessment of the dynamics of information impact without creating physical
analogues.
In our opinion, the proposed options for hybrid systems of the dynamics of
the distribution of information levels based on the diffusion equation using special
dynamic models are of certain interest and can be further refined taking into
account new formal and informal relationships that use various ways of
formalizing the external information influence.
Prospects for further research are the development of new diffusion-type
models that formalize the different nature of the influence of external factors on
the processes of information dissemination, the study of the influence of delay
and impulsive effects on the information process.
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INFORMATION ON THE ARTICLE
Eugene V. Ivokhin, ORCID: 0000-0002-5826-7408, Taras Shevchenko National
University of Kyiv, Ukraine, e-mail: ivohin@univ.kiev.ua
Larisa T. Adzhubey, ORCID: 0000-0002-8103-9657, Taras Shevchenko National
University of Kyiv, Ukraine, e-mail: adzhubey@ukr.net
Yuriy O. Naumenko, ORCID: 0000-0002-2631-1048, Taras Shevchenko National
University of Kyiv, Ukraine, e-mail: yura.was.here@gmail.com
Mykhailo F. Makhno, ORCID: 0000-0002-5826-7408, Taras Shevchenko National
University of Kyiv, Ukraine, e-mail: makhnom@gmail.com
ПРО ОДИН ПІДХІД ДО ЗАСТОСУВАННЯ ДРОБОВОГО АНАЛІЗУ ДЛЯ
МОДЕЛЮВАННЯ ПРОЦЕСІВ ІНФОРМАЦІЙНОГО ПОШИРЕННЯ /
Є.В. Івохін, Л.T. Aджубей, Ю.О. Науменко, M.Ф.Maхнo
Анотація. Розглянуто методику побудови моделі та метод знаходження
розв’язків у задачі імітаційного моделювання процесу поширення інформації
на основі використання крайової задачі для дробово-диференціального рівнян-
ня в частинних похідних. В основу покладено методику аналогій для моделю-
вання процесів інформаційного поширення, яка базується на використанні
особливостей дробового аналізу та дифузійного характеру процесів проник-
нення інформації. Запропоновано спосіб побудови гібридних моделей, що до-
зволяє враховувати зміни у часі граничних значень просторової змінної. Роз-
глянуто однорідні та неоднорідні моделі дифузійних процесів, які дали змогу
числено отримувати й аналізувати експериментальні дані для вирішення за-
вдання моніторингу рівнів поширення інформації в соціальних групах.
Kлючові слова: інформація, поширення, моделювання, диффузійні гібридні
моделі, дробовий аналіз.
ОБ ОДНОМ ПОДХОДЕ К ИСПОЛЬЗОВАНИЮ ДРОБНОГО АНАЛИЗА
ДЛЯ МОДЕЛИРОВАНИЯ ПРОЦЕССОВ ИНФОРМАЦИОННОГО
РАСПРОСТРАНЕНИЯ / E.В. Ивохин, Л.T. Aджубей, Ю.A. Науменко, M.Ф. Maхнo
Аннотация. Рассмотрены методика построения модели и метод нахождения
решений в задаче имитационного моделирования процесса распространения
информации на основе использования краевой задачи для дробно-
дифференциального уравнения в частных производных. Предлагается исполь-
зовать методику аналогий для моделирования процессов информационного
распространения, которая базируется на использовании особенностей дробно-
го анализа и диффузного характера процессов проникновения информации.
Предложен способ построения гибридных моделей, позволяющий учитывать
изменения во времени предельных значений пространственной переменной.
Рассмотрены однородные и неоднородные модели диффузионных процессов,
On one approach to using of fractional analysis for hybrid modeling of information …
Системні дослідження та інформаційні технології, 2021, № 4 137
позволяющие численно получать и анализировать экспериментальные данные
для решения задачи мониторинга уровней распространения информации в со-
циальных группах.
Kлючевые слова: информация, распространение, моделирование, диффузи-
онные гибридные модели, дробный анализ.
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| id | journaliasakpiua-article-232740 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:27:11Z |
| publishDate | 2021 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/01/7e6cd75e29616d6f19648849e5810b01.pdf |
| spelling | journaliasakpiua-article-2327402022-06-20T14:19:48Z On one approach to using of fractional analysis for hybrid modeling of information distribution processes Об одном подходе к использованию дробного анализа для моделирования процессов информационного распространения Про один підхід до застосування дробового аналізу для моделювання процесів інформаційного поширення Ivokhin, Eugene Adzhubey, Larisa Naumenko, Yuriy Makhno, Mykhailo информация распространение моделирование диффузионные гибридные модели дробный анализ інформація поширення моделювання диффузійні гібридні моделі дробовий аналіз information dissemination modeling diffusion hybrid models fractional analysis The article discusses a technique for constructing a model and a method for finding solutions in the problem of imitating the process of information dissemination based on the use of a boundary value problem for a fractional differential equation in partial derivatives. It is proposed to use the analogy technique for modeling information dissemination processes, which is based on the use of the features of a fractional analysis and the diffuse nature of information penetration processes. A method for constructing hybrid models is proposed, which makes it possible to take into account changes in the interval of values of the spatial variable over time. Homogeneous and inhomogeneous models of diffusion processes are considered, which make it possible to numerically obtain and analyze experimental data for solving problems of monitoring the levels of information dissemination in social groups. Рассмотрены методика построения модели и метод нахождения решений в задаче имитационного моделирования процесса распространения информации на основе использования краевой задачи для дробно-дифференциального уравнения в частных производных. Предлагается использовать методику аналогий для моделирования процессов информационного распространения, которая базируется на использовании особенностей дробного анализа и диффузного характера процессов проникновения информации. Предложен способ построения гибридных моделей, позволяющий учитывать изменения во времени предельных значений пространственной переменной. Рассмотрены однородные и неоднородные модели диффузионных процессов, позволяющие численно получать и анализировать экспериментальные данные для решения задачи мониторинга уровней распространения информации в социальных группах. Розглянуто методику побудови моделі та метод знаходження розв’язків у задачі імітаційного моделювання процесу поширення інформації на основі використання крайової задачі для дробово-диференціального рівняння в частинних похідних. В основу покладено методику аналогій для моделювання процесів інформаційного поширення, яка базується на використанні особливостей дробового аналізу та дифузійного характеру процесів проникнення інформації. Запропоновано спосіб побудови гібридних моделей, що дозволяє враховувати зміни у часі граничних значень просторової змінної. Розглянуто однорідні та неоднорідні моделі дифузійних процесів, які дали змогу числено отримувати й аналізувати експериментальні дані для вирішення завдання моніторингу рівнів поширення інформації в соціальних групах. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2021-12-22 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/232740 10.20535/SRIT.2308-8893.2021.4.10 System research and information technologies; No. 4 (2021); 128-137 Системные исследования и информационные технологии; № 4 (2021); 128-137 Системні дослідження та інформаційні технології; № 4 (2021); 128-137 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/232740/249649 |
| spellingShingle | інформація поширення моделювання диффузійні гібридні моделі дробовий аналіз Ivokhin, Eugene Adzhubey, Larisa Naumenko, Yuriy Makhno, Mykhailo Про один підхід до застосування дробового аналізу для моделювання процесів інформаційного поширення |
| title | Про один підхід до застосування дробового аналізу для моделювання процесів інформаційного поширення |
| title_alt | On one approach to using of fractional analysis for hybrid modeling of information distribution processes Об одном подходе к использованию дробного анализа для моделирования процессов информационного распространения |
| title_full | Про один підхід до застосування дробового аналізу для моделювання процесів інформаційного поширення |
| title_fullStr | Про один підхід до застосування дробового аналізу для моделювання процесів інформаційного поширення |
| title_full_unstemmed | Про один підхід до застосування дробового аналізу для моделювання процесів інформаційного поширення |
| title_short | Про один підхід до застосування дробового аналізу для моделювання процесів інформаційного поширення |
| title_sort | про один підхід до застосування дробового аналізу для моделювання процесів інформаційного поширення |
| topic | інформація поширення моделювання диффузійні гібридні моделі дробовий аналіз |
| topic_facet | информация распространение моделирование диффузионные гибридные модели дробный анализ інформація поширення моделювання диффузійні гібридні моделі дробовий аналіз information dissemination modeling diffusion hybrid models fractional analysis |
| url | https://journal.iasa.kpi.ua/article/view/232740 |
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