Two Kinds Of Time-Space Fractional Evolution Equations

In this thesis,we consider the global existence and finite time blow-up of positive solutions to the following time fractional evolution equation(?)(?)(?)and the time-space fractional evolution equation(?)(?)(?)supplemented with the initial condition u0,v0≥0,parameters 0<γ,δ<1,p,q,m,n>1,0<β<2.The operators(?)are defined by(?)(?)where F-1 is the inverse of the Fourier transfer F,and Γ is the Euler gamma function.We firstly apply the contraction mapping principle to get existence and uniqueness of the solutions.Secondly,by contradiction and by constructing suitable text functions,con-ditions for finite time blow-up of solutions are concluded.Finally,based on the series of fundamental inequalities,we establish necessary conditions for global existence solutions and the relationship between the maximum time of solutions and initial data and parameters.