Economic and mathematical modeling of environmental pollution of regional territories

The article is devoted to the construction of production functions using the methods of the theory of fractional derivatives used to assess environmental pollution factors, taking into account the totality of global environmental and economic challenges. When constructing the economic and mathematical model under study, two main criteria of a green economy are taken into account: ensuring the preservation of the environment and improving the quality of life of the population. For the first time, when modeling such problems, instead of the classical objective function, the model uses a two-factor Cobb–Douglas production function of a special type, taking into account the fractal nature of the environmental space. The work proves that the model can be reduced to a differential equation with a fractional derivative of the Caputo type, which has a regular solution for certain values of the coefficients and exponents of the production function.