Study on the effect of environmental pollution based on a fractional derivative resource depletion model

The effect of resource usage on economic growth has been investigated in many papers and the generic effect of resource usage efficacy by improving technical skills has been discussed. However, the impact of environmental pollution and the effect of memory property of the economic variables on economic growth have not been studied in detail. In this paper, a new resource depletion model, in which fractional derivative describes the memory property of economic variables, is built. Firstly, the influence of the environmental pollution on economic growth is analyzed. The results show the model is extreme sensitive to some parameters with considering the impact of environmental pollution. The small change of the parameters can lead a collapse of the economy in a short time. Meanwhile, new equilibrium region of economic growth can be obtained with considering the effect of the memory property of economic variables. Secondly, the effect of externally stochastic perturbation on the average of capital is studied, and the result shows random excitation can not only impede but also promote the development of the economy.