Fractal and Fractional Diffusion Equations of Price Changing of Commodity

Author(s)
Tianquan Yun

Affiliation(s)

School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, China.

School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, China.

ABSTRACT

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 x_{i }and x_{j} 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 inChina are given with same market data as [1]. Conclusion is made.

Cite this paper

T. Yun, "Fractal and Fractional Diffusion Equations of Price Changing of Commodity,"*Applied Mathematics*, Vol. 4 No. 7, 2013, pp. 18-22. doi: 10.4236/am.2013.47A005.

T. Yun, "Fractal and Fractional Diffusion Equations of Price Changing of Commodity,"

References

[1] T. Q. Yun, “Instant Diffusion Equation of Price Changing and Time—Space Exchanging Description,” Technology and Investment, Vol. 2, No. 2, 2011, pp. 124-128. doi:10.4236/ti.2011.22012

[2] G. Jumarie, “Probability Calculus of Fractional Order and Fractional Taylor’s Series and Application to FekkerPlanck Equation and Information of Non-Random Equations,” Chaos, Solitons & Fractals, Vol. 40, No. 3, 2009, pp. 1428-1448. doi:10.1016/j.chaos.2007.09.028

[3] W. Chen, H. G. Sun, X. D. Zhang and D. KoroSak, “Anomalous Diffusion Modeling by Fractal and Fractional Derivatives,” Computers and Mathematics with Applications, Vol. 59, No. 5, 2010, pp. 1754-1758. doi:10.1016/j.camwa.2009.08.020

[4] Editors of Mathematical Hand Book, “Hand Book of Mathematics,” High Education Publishers, Beijing, 1979.

[5] T. Q. Yun, “Calculation of Changing of Holding Shares or Currencies by Instant Diffusion Equation of Price Changing with Multiple Sources,” Modern Economy, Vol. 3, No. 5, 2012, pp. 522-525. doi:10.4236/me.2012.35068

[6] T. Q. Yun, “Applications of Heat Diffusion Equation and g-Contractive Mapping—Diffusion of Price Changing of Commodity, Analysis of Shares-Prices of A & H Stock Market, Strategy of Shares Dealing,” Lambert Academic Publishing, Germany, 2013. http://www.morebooks.de/store/gb/book/applications-of-heat-diffusion-equation-and-g-contractive-mapping/isbn/978-3-659-36845-5

[1] T. Q. Yun, “Instant Diffusion Equation of Price Changing and Time—Space Exchanging Description,” Technology and Investment, Vol. 2, No. 2, 2011, pp. 124-128. doi:10.4236/ti.2011.22012

[2] G. Jumarie, “Probability Calculus of Fractional Order and Fractional Taylor’s Series and Application to FekkerPlanck Equation and Information of Non-Random Equations,” Chaos, Solitons & Fractals, Vol. 40, No. 3, 2009, pp. 1428-1448. doi:10.1016/j.chaos.2007.09.028

[3] W. Chen, H. G. Sun, X. D. Zhang and D. KoroSak, “Anomalous Diffusion Modeling by Fractal and Fractional Derivatives,” Computers and Mathematics with Applications, Vol. 59, No. 5, 2010, pp. 1754-1758. doi:10.1016/j.camwa.2009.08.020

[4] Editors of Mathematical Hand Book, “Hand Book of Mathematics,” High Education Publishers, Beijing, 1979.

[5] T. Q. Yun, “Calculation of Changing of Holding Shares or Currencies by Instant Diffusion Equation of Price Changing with Multiple Sources,” Modern Economy, Vol. 3, No. 5, 2012, pp. 522-525. doi:10.4236/me.2012.35068

[6] T. Q. Yun, “Applications of Heat Diffusion Equation and g-Contractive Mapping—Diffusion of Price Changing of Commodity, Analysis of Shares-Prices of A & H Stock Market, Strategy of Shares Dealing,” Lambert Academic Publishing, Germany, 2013. http://www.morebooks.de/store/gb/book/applications-of-heat-diffusion-equation-and-g-contractive-mapping/isbn/978-3-659-36845-5