The study of the impact of the availability of renewable energy sources (RES) on the competitiveness and cost reduction opportunities is an actual objective for agro-industrial enterprises in the present time. The purpose of this paper was to develop a methodological approach based on a questionnaire survey, an integrated indicator of enterprise competitiveness, a model for assessing energy conservation costs, and regression analysis combined with a hierarchical synthesis of 20 Russian agro-industrial companies. The solution of the problem of nonlinear optimization of agro-industrial companies made it possible to determine the excess of the competitiveness criterion over the criterion of energy conservation cost reduction as a result of the use of RES. The conducted regression analysis showed a close relationship between the competitiveness of the companies under study and the availability of RES. Modeling and hierarchical synthesis of the study results confirmed that the use of RES in the activities of agro-industrial companies stimulates their competitive potential reflected by the competitiveness index and minimizes energy conservation costs. It was also found that there is an inverse regression relationship with a high degree of correlation between the provision of RES and the cost of energy-saving measures. Hence, it can be argued that a greater emphasis on the provision of Russian agro-industrial enterprises with RES can lead to their more sustainable and efficient development due to increased competitiveness and better cost reduction strategies.
This paper presents the results of applying a new iterative method to linear and nonlinear fractional partial differential equations in fluid mechanics. A numerical analysis was performed to find an exact solution of the fractional wave equation and fractional Burgers’ equation, as well as an approximate solution of fractional KdV equation and fractional Boussinesq equation. Fractional derivatives of the order α are described using Caputo's definition with 0 < α ≤ 1 or 1 < α ≤ 2. A comparative analysis of the results obtained using a new iterative method with those obtained by the Adomian decomposition method showed the first method to be more efficient and simple, providing accurate results in fewer computational operations. Given its flexibility and ability to solve nonlinear equations, the iterative method can be used to solve more complex linear and nonlinear fractional partial differential equations.
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