Study of Fractal and Fractional Diffusion Equations of Price Changing of Commodity

In this paper, three types of modeling of diffusion equations for price changing of commodity are
studied. In which, the partial derivatives of price of commodity respected to time on the left hand side
are integer-derivative, fractal derivative, and fractional derivative respectively; while just a second
order derivative respected to space is considered on the right hand side. The solutions of these
diffusion equations are obtained by method of departing variables and initial boundary conditions, by
translation of variables, and by translation of operators. The definitions of order of commodity x and
the distance between commodity xi and xj are defined as [1]. Examples of calculation of price of pork,
beef and mutton mainly due to price raising of pork in 2007-07 to 2008-02 in China are given with
same market data as [1]. Conclusion is made.