INFLUENCE OF MEMORY EFFECTS ON WORLD ECONOMY AND BUSINESS
The article discusses the influence of memory effects on the dynamics of world and national economics. The memory effects mean a dependence of economic processes not only on the current state of the economics, but also on the history of changes its state in the past. It is proposed to take into account that the economic agents can remember the history of changes of endogenous and exogenous variables on a finite time interval. Using the mathematical theory of derivatives and integrals of non-integer order, we build a simple dynamic model of the economics that takes into account the effects of memory with one-parameter power-law fading. We find solutions to this equation and proved the dependence of growth and decline of the economics from the effects of memory. It is shown that the inclusion of the memory effect can lead to a slowdown of economic growth, and to its growth instead of downturn, according to the indicator of memory decay. Memory effects with fading order 0<α<1 always lead to the suppression of economic growth regardless of the magnitude of the initial income, independent of costs and limit value of savings. Memory effects with fading order 1<α<2 results in the acceleration of economic growth, compared with the standard model, which ignores memory effects.