Geodesic
Mathematical model of dynamics of small enterprises with account of memory effects
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 26 (2019) no. 1, pp. 46-53 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper proposes a new mathematical model of the dynamics of small enterprises with the participation of foreign investment, which takes into account the memory effect and affects the rate of change in the value of production assets. This memory effect can be considered as a property of the economic environment, for example, the influence on the production of external factors, in which the cost of production assets will depend on its previous values. This non-local effect can be written in terms of a fractional order derivative. In this paper, we will assume that the order of the fractional derivative is a function of time. Therefore, we will solve the initial model equation using numerical methods of the theory of finite difference schemes. Further, in the work, visualization and interpretation of the calculation result was carried out.
Keywords: small enterprise dynamics, memory, model, fractional derivative. 
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     title = {Mathematical model of dynamics of small enterprises with account of memory effects},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
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E. A. Gafurova; Y. L. Michaylov; Y. V. Grushko; R. I. Parovik; I. A. Kashutina. Mathematical model of dynamics of small enterprises with account of memory effects. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 26 (2019) no. 1, pp. 46-53. http://geodesic.mathdoc.fr/item/VKAM_2019_26_1_a3/

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