Quasi Wavelet Method For The Space Order Fractional Partial Differential Equation

Fractional order differential equation is a differential equation contain-ing non-integer derivative. Researchers who found that the fractional order differential equation is well suited to describe the real life problems with mem-ory and genetic characteristics in the past ten years. Fractional order dif-ferential equation is better than integer order differential equation because it can simulate many natural physical processes and dynamic system pro-cesses, such as:the fractal theory and dispersion in porous media, capac-itance, electrolytic chemical, semiconductor physics, turbulence, condensed matter physics, viscoelastic system, biological mathematical and statistical mechanics, and so on. As present, there are many articles about the research of fractional order differential equation abroad. They are listed as follow-ing. Liu Fawang[12.13,15,19], Meerschaert[14], Tadjeran[16], Ervin[l7], Zhuang Pinghui[18], Chen Shiping[20,21]. Most of these studies adopt vari-ational method, variable transformation, the finite difference method and line method to study the numerical solution for the space order fractional partial differential equation. However, researches by using quasi wavelet algorithm to solve numerical approximation of these equations are rare. So in this paper, we adopt the method of quasi wavelet numerical to solve the one-dimensional fractional percolation equation with initial-boundary value problems and to demonstrate the reliability and validity of wavelet method for solving such e-quations by using numerical examples. Euler method is used to discrete time and quasi wavelet method is used to discrete space. The main content of the this paper is arranged as follows.Chapter one and chapter two introduce fractional order partial differential equation of some research findings and related knowledge about the fractional order derivative respectively. Chapter three introduces the development and theory of wavelet analysis. The fourth chapter focuses on wavelet function approximation. The fifth chapter gives the semi-discrete format and fully time-space discrete format of the one-dimensional fractional penetration equation. Numerical examplesare given and analyzed in chapter six.