Several Kinds Of Fractional Order Reaction Diffusion Equations And Related Problemsy

According to the content,this paper is mainly divided into three parts:A Cauchy problem of a class of time fractional diffusive wave equations is studied in the first part.We first solve the formal solution of the time fractional-order diffusive wave equation by the separation variable method.Secondly,we prove the existence theorem of Cauchy problem by using the correlation property of Fourier transformation and Mittag-Leffler function and Mainardi function.In the second part,we study the existence and uniqueness of the solutions of a class of time fractional-order diffusion equations.We prove the existence and uniqueness of the solution of the time fractional order diffusion equation by the method of separating variables and Fourier series expansion.In the third part,we study the Cauchy problem of the fractional Laplace expo-nential nonlinear heat equation.We use the density of C0?(Rn)to divide the initial condition of exp L0p(Rn)into a smooth part and a small part of exp Lp(Rn).We use the Banach fixed point theorem to prove the local well-being of the fractional Laplace exponential nonlinear heat equation in C([0,T];exp L0p(Rn))and the global existence of the solution in L?((0,?);expL0p(Rn))and give the solution in Lq(Rn)Estimation of attenuation on.