Research on the law of spatial fractional calculus diffusion equation in the evolution of chaotic economic system

Abstract

Abstract The development and evolution of economic system is the important support for economic analyses and researches. The application of nonlinear science, which is represented by chaos theory and has undergone major changes, makes people understand the ideological pivots and theoretical perspectives of the economic system that also includes the recognition of industrial economic system evolution. As a mathematical tool, fractional calculus has gradually penetrated into the economic field from the purely mathematical category. Based on the shift Chebyshev-tau idea, this paper solved a series of fractional diffusion equations with boundary conditions; using the tau method, the chaotic economic evolution is transformed into an algebraic equation system, and the equation’s approximate solution is obtained by combining these boundary conditions. On the basis of discovering chaotic characteristics in economic system evolution, the law of economic development and evolution is recognized by applying the perspective analysis of chaos theory. The results show that the spatial fractional calculus diffusion equation can effectively reveal the essence of economic system evolution and provide a new reference for the analysis mode of economic theories.