Analysis of fractional anomalous diffusion caused by an instantaneous point source in disordered fractal media

A theoretical analysis of fractional anomalous diffusion caused by an instantaneous point source in disordered fractal media is studied. Using the method of symmetry group of scaling transformations and the HH-function, the analytical solutions of concentration distribution are given. At the same time we derive the expressions of scattering function spectrum.The result shows that the scattering function spectra still have the properties of scaling function. The scattering functions of point source, line source and area source in regular Euclidean space can be regarded as particular cases of this paper and are included in this paper. At the end of the paper we discuss the asymptotic behaviors of the solution in detail. The results of this paper can be taken to be the fundamental solutions for every kind of boundary value problems of fractional anomalous diffusion in disordered fractal media.