MATHEMATICAL MODELING OF INFLATION PROCESSES IN THE ECONOMY USING DIFFERENTIAL EQUATIONS WITH FRACTIONAL DERIVATIVES

B a c k g r o u n d . When studying rapidly changing inflationary processes in economics, theoretical methods based on ordinary differential equations or partial differential equations are often used. However, as demonstrated in this paper, in certain cases it is more appropriate to use the apparatus of differential equations with fractional derivatives. This is due to the presence of various types of nonlinearities in functional relationships within inflationary processes, the influence of parameter values from previous time points on current values, the existence of scaling relations, and so on. In fact, all these characteristics are inherent to fractional calculus. M e t h o d s . The article is devoted to the application of differential equations with fractional derivatives of Caputo for the analysis of inflationary (deflationary) processes in the economy, based on the method of measuring inflation using the consumer price index, which takes into account changes in prices for a certain set of goods and services. This is demonstrated by changes in the specified index over finite time periods. R e s u l t s . It is shown that the use of fractional order differential equations can be useful for building flexible tools for forecasting inflation/deflation processes. The relationship between the inflation rate and the unemployment rate is also investigated. C o n c l u s i o n s . It has been established that the change in the fractional derivative index in theoretical models of economic processes allows describing different regimes of price dynamics – from moderate inflation to galloping and hyperinflation, as well as complex deflationary scenarios. The appearance of negative values of price indices for individual goods can be interpreted as a consequence of their excess production, which leads to a loss of market value. The proposed method of using differential equations with fractional values of the order of derivatives provides an expansion of the possibilities of modeling a wide range of economic processes.