The Fox function expression and the analytic expression for the concentration distribution of fractional anomalous diffusion caused by an instantaneous point source in n_dimensional space(n=1,2 or 3)are derived by means of the condition of mass conservation,the time_space similarity of the solution,Mellin transform and the properties of the Fox function.

The analytic expression and the asymptotic properties for the concentration distribution of the anomalous diffusion with fractional order caused by a instantaneous point source in 3-dimmentional space are obtained by means of the time-space similarity for the solution,the law of conservation of mass,Mellin transform and the properties of Fox functions.

Starting with the fractional viscoelastic theory,a binary mathematical model is put forward to describe the degradation rule of properties of stress relaxation and compression set of vulcanite during the thermo-oxidative aging by means of Fox-H function.